共查询到20条相似文献，搜索用时 343 毫秒
1.
This paper deals with the problem of robust stability and robust stabilization for a class of continuous-time singular Takagi–Sugeno fuzzy systems. Sufficient conditions on stability and stabilization are proposed in terms of strict LMI (Linear Matrix Inequality) for uncertain T–S fuzzy models. In order to reduce the conservatism of results developed using quadratic method, an approach based on non-quadratic Lyapunov functions and S-procedure is proposed. Illustrative examples are given to show the effectiveness of the given results. 相似文献
2.
Finite-time robust control of a class of nonlinear time-delay systems via Lyapunov functional method
This paper investigates the finite-time robust control problem of a class of nonlinear time-delay systems with general form, and proposes some new delay-independent and delay-dependent conditions on the issue. First, by developing an equivalent form, the paper studies finite-time stabilization problem, and presents some delay-dependent stabilization results by constructing suitable Lyapunov functionals. Then, based on the stabilization results, we study the finite-time robust control problem for the systems, and give a robust control design procedure. Finally, the study of two illustrative examples shows that the results obtained of the paper work well in the finite-time stabilization and robust stabilization for the systems. It is shown that, by using the method in the paper, the obtained results do not contain delay terms, which can avoid solving nonlinear mixed matrix inequalities and reduce effectively computational burden. Moreover, different from existing finite-time results, the paper also presents delay-dependent sufficient conditions on the finite-time control problem for the systems. 相似文献
3.
A class of networked nonlinear control systems with norm-bounded uncertainties is presented in this paper. The class is represented by Takagi–Sugeno (T-S) fuzzy models with packet processing. The network loop delay is considered either as known delay or random delay. For the former case, we develop conditions that guarantee the robust asymptotic stability and state-feedback stabilization with strict dissipativity and cast the results in linear matrix inequality (LMI) framework. Next employing a probabilistic-based delay partitioning method to deal with random delay, we establish novel LMI criteria for strict dissipative stability analysis and feedback synthesis. The efficacy of the ensuing techniques is demonstrated by numerical solution of typical examples and Mont Carlo simulation. 相似文献
4.
In this paper we consider a class of fractional order linear time invariant (FO-LTI) interval systems with linear coupling relationships among the fractional order, the system matrix and the input matrix. We present the sufficient conditions for the robust stability and stabilization of such coupling FO-LTI interval systems with the fractional order α satisfying 0<α<1. All the results are proposed in terms of linear matrix inequalities (LMI). Two numerical examples show that our results are effective for checking the robust asymptotical stability and designing the stabilizing controller for FO-LTI interval systems. 相似文献
5.
In this paper, we first deal with the robust stability of uncertain linear stochastic differential delay systems. The parameter uncertainties are time-varying and unknown but are norm-bounded via two types of uncertainties, and the delays are time invariant. We then extend the proposed theory to discuss the robust stabilization of uncertain stochastic differential delay systems. These results are given in terms of linear matrix inequalities. Two examples are presented to illustrate the effectiveness. 相似文献
6.
Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. Since finite-time convergence implies nonuniqueness of system solutions in reverse time, such systems possess non-Lipschitzian dynamics. Sufficient conditions for finite-time stability have been developed in the literature using Hölder continuous Lyapunov functions. In this paper, we develop a general framework for finite-time stability analysis based on vector Lyapunov functions. Specifically, we construct a vector comparison system whose solution is finite-time stable and relate this finite-time stability property to the stability properties of a nonlinear dynamical system using a vector comparison principle. Furthermore, we design a universal decentralized finite-time stabilizer for large-scale dynamical systems that is robust against full modeling uncertainty. Finally, we present two numerical examples for finite-time stabilization involving a large-scale dynamical system and a combustion control system. 相似文献
7.
《Journal of The Franklin Institute》2021,358(16):8377-8395
The usage of communication networks provides a backbone of integration of information technologies and load frequency control (LFC) scheme. Time delays introduced by network environments taking the new challenge for dynamic performances and even the stability of closed-loop LFC scheme. This paper focuses on the stability and stabilization of multi-area LFC schemes for power systems with the introduction of communication networks and renewable energies. Markov theory is exploited in this paper for describing the discrete time-delay mechanism. Then, by utilizing Wirtinger-based inequality, and constructing a novel Lyapunov functions, the results of robust stability and stabilization criteria are derived in terms of linear matrix inequality (LMI). Finally, simulation results are provided to demonstrate the effectiveness and superiority of developed results. 相似文献
8.
Renming Yang Liying Sun Guangyuan Zhang Qiang Zhang 《Journal of The Franklin Institute》2019,356(12):5961-5992
This paper investigates the finite-time stability (FTS) and finite-time stabilization for a class of nonlinear singular time-delay Hamiltonian systems, and proposes a number of new results on these issues. Firstly, an equivalent form is obtained for the nonlinear singular time-delay Hamiltonian systems by the singular matrix decomposition method, based on which some delay-independent and delay-dependent conditions on the FTS are derived for the systems by constructing a kind of novel Lyapunov function. Secondly, we use the equivalent form as well as the energy shaping plus damping injection technique to investigate the finite-time stabilization problem for a class of nonlinear singular port-controlled Hamiltonian (PCH) systems with time delay, and present a specific control design procedure for the systems. Finally, we give several illustrative examples to show the effectiveness of the results obtained in this paper. 相似文献
9.
Le V. Hien 《Journal of The Franklin Institute》2009,346(6):611-625
This paper presents new exponential stability and stabilization conditions for a class of uncertain linear time-delay systems. The unknown norm-bounded uncertainties and the delays are time-varying. Based on an improved Lyapunov-Krasovskii functional combined with Leibniz-Newton formula, the robust stability conditions are derived in terms of linear matrix inequalities (LMIs), which allows to compute simultaneously the two bounds that characterize the exponential stability rate of the solution. The result can be extended to uncertain systems with time-varying multiple delays. The effectiveness of the two stability bounds and the reduced conservatism of the conditions are shown by numerical examples. 相似文献
10.
This paper investigates the problem of global stabilization of switched nonlinear systems in non-triangular form whose subsystems are not assumed to be asymptotically stabilizable. The use of multiple Lyapunov functions (MLFs) method permits removal of a common restriction in which the nonlinear structures in the non-switched nonlinear systems are restricted to a triangular structure when applying backstepping. Using the MLFs method and the adding a power integrator technique, we design state-feedback controllers for individual subsystems and construct a switching law to guarantee asymptotic stability of the closed-loop switched system. As an application of the proposed design method, the global stabilization problem of a continuously stirred tank reactor (CSTR) system and two inverted pendulums which cannot be handled by the existing methods is investigated. 相似文献
11.
This paper deals with the problems of non-fragile robust stochastic stabilization and robust H∞ control for uncertain stochastic nonlinear time-delay systems. The parameter uncertainties are assumed to be time-varying norm-bounded appearing in both state and input matrices. The time-delay is unknown and time-varying with known bounds. The non-fragile robust stochastic stabilization problem is to design a memoryless non-fragile state feedback controller such that the closed-loop system is robustly stochastically stable for all admissible parameter uncertainties. The purpose of robust H∞ control problem, in addition to robust stochastical stability requirement, is to reduce the effect of the disturbance input on the controlled output to a prescribed level. Using the Lyapunov functional method and free-weighting matrices, delay-dependent sufficient conditions for the solvability of these problems are established in terms of linear matrix inequality (LMI). Numerical example is provided to show the effectiveness of the proposed theoretical results. 相似文献
12.
This paper studies the finite-time stability and stabilization of linear discrete time-varying stochastic systems with multiplicative noise. Firstly, necessary and sufficient conditions for the finite-time stability are presented via a state transition matrix approach. Secondly, this paper also develops the Lyapunov function method to study the finite-time stability and stabilization of discrete time-varying stochastic systems based on matrix inequalities and linear matrix inequalities (LMIs) so as to Matlab LMI Toolbox can be used.The state transition matrix-based approach to study the finite-time stability of linear discrete time-varying stochastic systems is novel, and its advantage is that the state transition matrix can make full use of the system parameter informations, which can lead to less conservative results. We also use the Lyapunov function method to discuss the finite-time stability and stabilization, which is convenient to be used in practical computations. Finally, three numerical examples are given to illustrate the effectiveness of the proposed results. 相似文献
13.
针对几类重要的随机非线性系统, 提出了一些新的概念,发展了一些基本分析工具, 研究了几类控制器的设计问题. 主要成果包括:(1) 针对一类部分动态不可量测的非线性随机系统,引入了随机输入状态稳定(SISS)的概念, 借助于分析概率理论,发展了随机系统改变能量函数方法, 成功地处理了随机微分中的伊藤项,给出了随机非线性串联系统SISS的小增益类条件. (2) 对一类具有SISS随机逆动态的大规模随机非线性系统,给出了分散自适应输出反馈镇定控制器的构造性设计方法. 既解决了实用镇定问题也解决了渐近镇定问题. 在分散控制框架内,给出了处理随机非线性逆动 态的方法. (3) 对一类具有不稳定零动态的随机非线性系统,引入了随机输入状态可镇定的概念,给出了全局输出反馈镇定控制器构造性设计方法. (4) 对一类具有线性增长的不可量测状态的随机非线性系统,针对方差未知的噪声和一般随机输入,引入了广义随机输入状态稳定(GSISS)的概念,分别给出了随机干扰抑制和渐近镇定的输出反馈控制器的构造性设计方法.(5) 对一般的时滞随机非线性系统, 给出了解存在唯一的判定条件,引入了依概率全局(渐近)稳定的概念及相应的判定准则,丰富了随机时滞非线性系统的控制器设计理论. 对一类不确定随机时变时滞系统,构造性地设计出了自适应输出反馈镇定控制器. 相似文献
14.
《Journal of The Franklin Institute》2023,360(2):1184-1206
This paper proposes a robust switched model-based predictive controller design for discrete linear systems with state constraints, inputs, and disturbances limited in norm. Modeled via linear matrix inequalities, the online and offline designs of the proposed control aim at minimizing the upper bound of the quadratic performance index for a horizon of infinite prediction associated with the state estimator and the switching rule, seeking to guarantee the robust stability for closed-loop systems. To this end, three theorems are formulated. To demonstrate the effectiveness of the control strategy, a comparative analysis is performed between the performance of the proposed model and a benchmark method. From the results, it is possible to conclude that the proposed method is promising in the scope of control of linear systems subject to switching, being more efficient than the benchmark for the stabilization and control of both numerical examples. 相似文献
15.
The problem of robust stabilization for a class of dynamic systems with time-varying state delay as well as parametric and input uncertainties is considered in this paper. Several delay-independent stabilizability criteria and memoryless state feedback controllers are presented to guarantee the asymptotic stability of the closed-loop uncertain time-delay systems. It is shown that if all uncertainties and delay terms are matched, then the mentioned systems can always be stabilized, or can be stabilized with a specified decaying rate. 相似文献
16.
《Journal of The Franklin Institute》2022,359(2):1194-1214
Hyper-exponential stability analysis and hyper-exponential stabilization of linear systems by bounded linear time-varying feedback are investigated in this paper. On the one hand, we propose some Lyapunov-like hyper-exponential stability theorems (both global and local) based on the comparison principle and the concepts of hyper-exponentially stable functions and hyper-exponentially increasing functions. On the other hand, we establish methods to design bounded linear time-varying controllers such that hyper-exponential stability of linear time-invariant systems can be guaranteed. The key design tool is the utilization of a time-varying parameter contained in the controller and the properties of solution to a parametric Lyapunov equation. Both state feedback and observer-based output feedback are accommodated. As a further result, hyper-exponential semi-global stabilization for linear systems by bounded controls is discussed. Finally, the validity of the proposed schemes is illustrated through numerical simulations on spacecraft rendezvous control system. 相似文献
17.
Pin-Lin Liu 《Journal of The Franklin Institute》2010,347(8):1577-1588
This paper discusses the problems of delay-dependent stability and stabilization of neutral saturating actuator systems with constant or time-varying delays. The problems of stabilization for neutral saturating actuator system with time-varying delay and parameter from the presented results, the condition obtained here does not need derivative information of the delay time and thus can be used to analyze the stabilization problem for a class of saturating actuator systems with time-varying delay, which is bounded but arbitrarily fast time-varying. Using the model transformation and quasi-convex optimization problem, we derive delay-dependent conditions for the stability of systems in terms of the linear matrix inequality. The stabilization conditions are formulated as linear matrix inequalities (LMIs) which can be solved by convex optimization algorithm. Moreover, the stability criteria are extended to design a stabilizing state feedback controller. Numerical examples show that the results obtained in this paper significantly improve the estimate of stability limit over some existing results reported previously in the literature. 相似文献
18.
《Journal of The Franklin Institute》2023,360(12):8614-8632
This paper investigates the robust output regulation problem for stochastic systems with additive noises. As is known, for the output regulation control problem, a general method is to regard that the system is disturbed by an autonomous exosystem (which is consisted by external disturbances and reference signals), and for the system disturbed by the white noise, the stochastic differential equations (SDEs) should be utilized in modeling, accordingly, a controller with a feedforward regulator is constructed for the stochastic system with an exosystem, which can not only cancel the external disturbance, but also transform the trajectory tracking problem into the stabilization problem; In consideration of the state variables in stochastic systems cannot be measured completely, we embed an observer to the controller, such that the random interference can be suppressed, and the trajectory tracking can be achieved. Based on the stochastic control theory, the criteria of the exponential practical stability in the mean square is presented for the closed-loop system, finally, through tuning the controller parameters, the mean square of the tracking error can converge to an arbitrarily small neighborhood of the origin. 相似文献
19.
《Journal of The Franklin Institute》2021,358(13):6634-6665
This paper is concerned with stability analysis and stabilization of time-varying delay discrete-time systems in Lyapunov-Krasovskii stability analysis framework. In this regard, a less conservative approach is introduced based on non-monotonic Lyapunov-Krasovskii (NMLK) technique. The proposed method derives time-varying delay dependent stability conditions based on Lyapunov-Krasovskii functional (LKF), which are in the form of linear matrix inequalities (LMI). Also, a PID controller designing algorithm is extracted based on obtained NMLK stability condition. The stability of the closed loop system is guaranteed using the designed controller. Another property that is important along with the stability, is the optimality of the controller. Thus, an optimal PID designing technique is introduced in this article. The proposed method can be used to design optimal PID controller for unstable multi-input multi-output time-varying delay discrete-time systems. The proposed stability and stabilization conditions are less conservative due to the use of non-monotonic decreasing technique. The novelty of the paper comes from the consideration of non-monotonic approach for stability analysis of time-varying delay discrete-time systems and using obtained stability conditions for designing PID controller. Numerical examples and simulations are given to evaluate the theoretical results and illustrate its effectiveness compared to the existing methods. 相似文献
20.
R. Sakthivel R. Sakthivel V. Nithya P. Selvaraj O.M. Kwon 《Journal of The Franklin Institute》2018,355(14):6353-6370
This paper studies the robust stochastic stabilization problem for a class of fuzzy Markovian jump systems with time-varying delay and external disturbances via sliding mode control scheme. Based on the equivalent-input-disturbance (EID) approach, an online disturbance estimator is implemented to reject the unknown disturbance effect on the considered system. Specifically, to obtain exact EID estimation Luenberger fuzzy state observer and a low-pass filter incorporated to the closed-loop system. Moreover, novel fuzzy EID-based sliding mode control law is constructed to ensure the stability of the closed-loop system with satisfactory disturbance rejection performance. By employing Lyapunov stability theory and some integral inequalities, a new set of delay-dependent robust stability conditions is derived in terms of linear matrix inequalities (LMIs). The resulting LMI is used to find the gains of the state-feedback controller and the state observer a for the resulting closed-loop system. At last, numerical simulations based on the single-link arm robot model are provided to illustrate the proposed design technique. 相似文献