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1.
This paper is concerned with the exponential stabilization of switched linear systems subject to actuator saturation with both stabilizable subsystems and unstabilizable subsystems for continuous-time case and discrete-time case, respectively. Sufficient conditions for the exponential stabilization under dwell time switching under the cases of continuous-time and discrete-time are established by using a novel class of multiple time-varying Lyapunov function. The existence conditions for stabilizing controllers are presented in terms of linear matrix inequalities (LMIs) for the continuous-time case and the discrete-time case, respectively. Two optimization problems are proposed for obtaining the maximal attraction region. The problem of exponential stabilization for switched system subject to actuator saturation with asynchronous switching controller is also studied. Several numerical examples are presented to prove the validity of the obtained results. 相似文献
2.
《Journal of The Franklin Institute》2022,359(14):7733-7752
In this paper, the networked stabilization of discrete-time periodic piecewise linear systems under transmission package dropouts is investigated. The transmission package dropouts result in the loss of control input and the asynchronous switching between the subsystems and the associated controllers. Before studying the networked control, the sufficient conditions of exponential stability and stabilization of discrete-time periodic piecewise linear systems are proposed via the constructed dwell-time dependent Lyapunov function with time-varying Lyapunov matrix at first. Then to tackle the bounded time-varying packet dropouts issue of switching signal in the networked control, a continuous unified time-varying Lyapunov function is employed for both the synchronous and asynchronous subintervals of subsystems, the corresponding stabilization conditions are developed. The state-feedback stabilizing controller can be directly designed by solving linear matrix inequalities (LMIs) instead of iterative optimization used in continuous-time periodic piecewise linear systems. The effectiveness of the obtained theoretical results is illustrated by numerical examples. 相似文献
3.
This paper is concerned with the problem of state feedback stabilization of a class of discrete-time switched singular systems with time-varying state delay under asynchronous switching. The asynchronous switching considered here means that the switching instants of the candidate controllers lag behind those of the subsystems. The concept of mismatched control rate is introduced. By using the multiple Lyapunov function approach and the average dwell time technique, a sufficient condition for the existence of a class of stabilizing switching laws is first derived to guarantee the closed-loop system to be regular, causal and exponentially stable in the presence of asynchronous switching. The stabilizing switching laws are characterized by a upper bound on the mismatched control rate and a lower bound on the average dwell time. Then, the corresponding solvability condition for a set of mode-dependent state feedback controllers is established by using the linear matrix inequality (LMI) technique. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method. 相似文献
4.
Jinxing Lin Xudong Zhao Min Xiao Jingjin Shen 《Journal of The Franklin Institute》2019,356(4):2060-2089
This paper is concerned with state feedback stabilization of discrete-time switched singular systems with time-varying delays existing simultaneously in the state, the output and the switching signal of the switched controller. On the basis of equivalent dynamics decomposition and Lyapunov–Krasovskii method, exponential estimates for the response of slow states of the closed-loop subsystems running in asynchronous and synchronous periods are first given. Exponential estimates for the response of fast states are also provided by establishing an analytic equation to solve the fast states and using some algebraic techniques. Then, by employing the obtained exponential estimates and the piecewise Lyapunov function approach with average dwell time (ADT) switching, sufficient conditions for the existence of a class of stabilizing switching signals and state feedback gains are derived, which explicitly depend on upper bounds on the delays and a lower bound on the ADT. Finally, two numerical examples are provided to illustrate the effectiveness of the obtained theoretical results. 相似文献
5.
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
6.
《Journal of The Franklin Institute》2022,359(1):66-83
This paper studies the exponential stability of switched positive system consisting of unstable subsystems with distributed time-varying delay. Unlike the existing results concerning delays, switching behaviors dominating the system can be either stabilizing or destabilizing. The distributed delay is supposed to be slowly varying and upper-bounded. To tackle the difficulties brought by both the switching behaviors with mixed effects and the distributed delay, a multiple discretized Lyapunov–Krasovskii functional is employed to derive sufficient conditions for the exponential stability of the system. Specifically, by adjusting the ratio of the stabilizing switching behaviors, the state divergence caused by unstable subsystems and destabilizing switching behaviors can be compensated. Simulation examples demonstrate the effectiveness of the results. 相似文献
7.
A backstepping-based adaptive neural network decentralized stabilization approach is presented for the expanding construction of a class of nonlinear large scale interconnected systems in this paper. The expanding construction of large scale interconnected systems is to add some new subsystems into the original system during the operation of the original system. For stabilization of the expanding system, it is more realistic to keep the decentralized control laws of the original subsystems unchanged. And the decentralized control laws of the new subsystems must be designed to stabilize both itself and the resultant large scale system. In this paper, neural networks are used to approximate the unknown nonlinear functions in the new subsystems and the unknown nonlinear interconnection functions. The decentralized control laws and the parameter adaptive laws of the new subsystems are designed by using backstepping technique for the expanding construction of the large-scale interconnected system. Based on Lyapunov stability theory, the uniform and ultimate boundedness of all signals in the closed-loop system is proved. Two illustrative examples show the feasibility of the presented approach. 相似文献
8.
9.
In this paper, a methodology is proposed for the design of Networked Distributed Sliding Mode Controllers (NDSMC) for large-scale systems consisting of interconnected discrete-time subsystems. The state of each of these subsystems has time varying delays and there is also delay and packet loss in their interconnection links. The Networked Distributed Control System (NDCS), which is subject to the non-idealities of these interconnection links, is modeled and a Linear Matrix Inequality (LMI) based sufficient condition for designing asymptotically stable sliding surfaces, as well as the stabilizing NDSMC, is proposed. Finally, the proposed NDSMC structure is employed for the formation control of Unmanned Aerial Vehicles (UAVs); in which five vehicles are flying in a leader–follower architecture, in two platoons, whilst attempting to maintain the desired speed with a constant desired Euclidean distance between successive vehicles despite the presence of external perturbations such as wind disturbances. 相似文献
10.
《Journal of The Franklin Institute》2022,359(10):4893-4914
This paper investigates the global stabilization of discrete-time linear systems with input time delay by bounded controls. Based on some special canonical forms containing time delays both in its input and state, two special discrete-time linear systems---multiple integrators and oscillators are first considered. The global stabilizing controllers are respectively established, and moreover, explicit conditions are established to guarantee the stability of the closed-loop systems. Subsequently, a concise design method is proposed for globally stabilizing general discrete-time linear system by combining the design methods for multiple integrators and oscillators. The designed controller is in the explicit form with explicit stability conditions being given, and thus is easier to use than the existing results. Finally, numerical simulations illustrate the effectiveness of the proposed approaches. 相似文献
11.
This paper focuses on the problem of semi-global output-feedback stabilization for a class of switched nonlinear time-delay systems in strict-feedback form. A switched state observer is first constructed, then switched linear output-feedback controllers for individual subsystems are designed. By skillfully constructing multiple Lyapunov–Krasovskii functionals and successfully solving several troublesome obstacles, such as time-varying delay and switching signals and nonlinearity in the design procedure, the switched linear output-feedback controllers designed can render the resulting closed-loop switched system semi-globally stabilizable under a class of switching signals with average dwell time. Furthermore, under some milder conditions on nonlinearities, the semi-global output-feedback stabilization problem for switched nonlinear time-delay systems is also studied. Simulation studies on two examples, which include a continuous stirred tank reactor, are carried out to demonstrate the effectiveness of the proposed approach. 相似文献
12.
This paper investigates the stability and stabilization of switched linear singular systems with state reset at switching instants. Based on the dynamics decomposition of singular subsystems, a sufficient stability condition for the system with the given state reset is obtained. Then, the stabilization problem by state reset is investigated and an algorithm for computing the reset matrices is presented. The obtained results extend some previous works on both singular switched systems and reset control for normal switched systems. Finally, a numerical example is presented to illustrate the effectiveness of the proposed approach. 相似文献
13.
This paper is concerned with the finite-time stabilization for a class of stochastic BAM neural networks with parameter uncertainties. Compared with the previous references, a continuous stabilizator is designed for stabilizing the states of stochastic BAM neural networks in finite time. Based on the finite-time stability theorem of stochastic nonlinear systems, several sufficient conditions are proposed for guaranteeing the finite-time stability of the controlled neural networks in probability. Meanwhile, the gains of the finite-time controller could be designed by solving some linear matrix inequalities. Furthermore, for the stochastic BAM neural networks with uncertain parameters, the problem of robust finite-time stabilization could also be ensured as well. Finally, two numerical examples are given to illustrate the effectiveness of the obtained theoretical results. 相似文献
14.
In this paper, the problem of stabilization for a class of switched delay systems with polytopic type uncertainties under asynchronous switching is investigated. When the switching of the controllers has a lag to the switching of subsystems, i.e. the switching signal of the switched controller involves delay, parameter-dependent Lyapunov functionals are constructed, which are allowed to increase during the running time of active subsystems with the mismatched controller. Based on the average dwell time method, sufficient conditions for exponential stability are developed for a class of switching signals. Finally, a river pollution control problem is given to demonstrate the feasibility and effectiveness of the proposed design techniques. 相似文献
15.
Xiandong Chen Xianfu Zhang Chenghui Zhang Le Chang 《Journal of The Franklin Institute》2018,355(9):3895-3910
In this paper, a novel control strategy is proposed for asymptotically stabilizing chained nonholonomic systems with input delay. Firstly, by using the input-state-scaling technique and the static gain control method, the stabilization control problem of such systems is transformed into designing two gain parameters to stabilize a class of generalized feedback systems with state delay. Then, based on the Lyapunov–Krasovskii theorem, the stability analysis of the closed-loop systems is achieved by the appropriate selection of the gain parameters, and the state and output feedback controllers are constructed simultaneously. An illustrative example is also provided to demonstrate the effectiveness of the proposed strategy. 相似文献
16.
This paper considers the simultaneous stabilization of a set of nonlinear systems, that involve uncertain nonlinearities besides multiple time-varying delays in the states. Under the assumption that the upper bounds of delays are known, a memoryless simultaneously stabilizing state feedback controller is presented by proposing a control Lyapunov-Krasovskii functional (CL-KF) method. As required to establish the CL-KF approach, a systematic procedure is given to construct CL-KFs for the systems under consideration. By the obtained CL-KFs, a common stabilizing state feedback control law is established to drive all the systems to the origin. Examples are finally given to verify the benefit of the proposed design method. 相似文献
17.
This paper studies the stability analysis problems of periodic piecewise systems, in which subsystems are given in the time-varying polynomial forms. A Lyapunov function with continuous time-varying Lyapunov matrix is adopted, which relaxes constraints on the variation of Lyapunov function in each subsystem. Using the time interval information, the exponential stability and stabilizing controller synthesis are studied. The results provide a possible alternative method to study the general periodic time-varying systems, which may further support the analysis and synthesis of general periodic systems. The effectiveness of the proposed method is validated and illustrated via numerical examples. 相似文献
18.
The problem of finite-time stability for linear discrete-time systems with time-varying delay is studied in this paper. In order to deal with the time delay, the original system is firstly transformed into two interconnected subsystems. By constructing a delay-dependent Lyapunov–Krasovskii functional and using a two-term approximation of the time-varying delay, sufficient conditions of finite-time stability are derived and expressed in terms of linear matrix inequalities (LMIs). The derived stability conditions can be applied into analyzing the finite-time stability and deriving the maximally tolerable delay. Compared with the existing results on finite-time stability, the derived stability conditions are less conservative. In addition, for the stabilization problem, we design the state-feedback controller. Finally, numerical examples are used to illustrate the effectiveness of the proposed method. 相似文献
19.
The paper is concerned with the modeling and stabilization problem of networked control systems under simultaneous consideration of bounded packet dropouts and occasionally missing control inputs. In particular, the focus of the paper is to capture the case where the packet dropouts and control inputs missing are subject to multiple sampling periods, and not periodic as in existing results. By input-delay approach and then fully considering the probability distribution characteristic of packet dropouts in the modeling, the original linear system is firstly transformed to a switched stochastic time-delay system. Meanwhile, the probability distribution values of stochastic delay taking values in m(m ≥ 2) given intervals can be explicitly obtained, which is of vital importance to analyse the stabilization problem of considered system. Secondly, by means of the average dwell time technique, some sufficient conditions in terms of linear matrix inequalities for the existence of desired stabilizing controller are derived. Finally, an illustrative example is given to illustrate the effectiveness of the proposed stabilizing controller and some less conservative results are obtained. 相似文献
20.
《Journal of The Franklin Institute》2022,359(8):3597-3613
This paper studies the globally almost surely exponential stabilization of discrete-time switched systems (DSSs) with infinitely distributed delay. On account of the limitation of communication resources in the actual environment, a novel class of observer-based quantized control scheme is designed that incorporates the quantization of three kinds of signals: the measurement output, the state of observer, and the measurement output of observer. By employing S-procedure and some matrix inequality techniques, an algorithm is given to design the controller parameters. To reduce the conservativeness of the obtained results, new multiple Lyapunov–Krasovskii functionals (LKFs) with negative terms are proposed to deal with the infinitely distributed delay and mode-dependent average dwell time (MDADT) switching based on transition probability (TP) is introduced to study the stabilization of DSSs with both stable and unstable modes. It is worth highlighting that the improved stabilization conditions for DSSs can release the restriction on the length of dwell time (DT) of stable and unstable subsystems. Finally, a simulation example is presented to demonstrate the validity of the proposed method. 相似文献