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1.
This paper is concerned with the stability analysis of linear systems with time-varying delays. First, by introducing the quadratic terms of time-varying delays and some integral vectors, a more suitable Lyapunov-Krasovskii functional (LKF) is constructed. Second, two new delay-dependent estimation methods are developed in the stability analysis of linear system with time-varying delays, which include a reciprocally convex matrix inequality and an integral inequality. More information about time-varying delays and more free matrices are introduced into the two estimation approaches, which play a key role for obtaining an accurate upper bound of the integral terms in time derivative of LKFs. Third, based on the novel LKFs and new estimation approaches, some less conservative criteria are derived in the form of linear matrix inequality (LMI). Finally, three numerical examples are applied to verify the advantages and effectiveness of the newly proposed methods.  相似文献   

2.
This paper is focused on delay-dependent stability problem of time-varying delay systems. By introducing delay-derivative-dependent slack matrices, relaxed stability conditions are derived based on Lyapunov-Krasovskii functional approach. As the delay-derivative-dependent slack matrices provide extra freedom to optimize the Lyapunov matrices, less conservative results are obtained. Two benchmark examples are provided to verify the effectiveness of the proposed approach.  相似文献   

3.
In this paper, the stability of grey discrete-time systems is discussed whose state matrices are interval matrices. A new approach is obtained which guarantee the stability of grey discrete-time systems. The sufficient condition for robust stability of grey time delay systems subjected to interval systems is also derived. By mathematical analysis, the stability criterion is less conservative than those in previous results. Examples are given to compare the proposed method with reported recently.  相似文献   

4.
In this paper, the observer-based state estimation of discrete-time Takagi-Sugeno fuzzy systems is enhanced markedly by developing a distinctive multi-instant gain-scheduling law. Firstly, the updated information of both the past-time and the current-time normalized fuzzy weighting functions is fused into the proposed multi-instant gain-scheduling law in a comprehensive way, and it is important to point out that those existing ones reported in the literature belong to special cases of ours. Secondly, a set of time-varying free matrices for constructing more relaxed fuzzy observers are introduced for the first time in accordance with different operating modes. Moreover, the time-varying free matrices are more general than those previous time-invariant ones and most of them no longer need to be positive or negative definite. Therefore, a significant reduction in conservatism can be achieved at the expense of a slight increase in offline computing burden over those competing approaches. Finally, a set of numerical simulations are implemented to verify the superiority of the designed approach.  相似文献   

5.
This paper is concerned with the quadratic stability analysis and robust distributed controllers design of both continuous-time and discrete-time uncertain spatially interconnected systems (USISs), where uncertainties are modeled by linear fractional transformation (LFT). The well-posedness, quadratic stability, and contractiveness of USISs are properly defined for the first time. A sufficient condition employing the given system matrices is established to check the well-posedness, quadratic stability and contractiveness. This condition is simpler than the existing conditions based on the decomposition of system matrices. Based on the new condition derived, a sufficient condition is given for the existence of robust distributed controllers and a constructive method is then presented for the design of robust distributed controllers. The advantage of the proposed constructive approach is that it employs the given system matrices while the existing methods conduct the bilinear transformation on these matrices when design controllers, and consequently, the constructive approach in this paper is computationally more efficient than the existing methods. Several examples are included to demonstrate the simplicity, efficiency and applicability of the derived theoretical results.  相似文献   

6.
This paper proposes novel conditions based on linear matrix inequalities (LMI) for stability analysis of arbitrarily-fast time-varying delays systems. The time-varying delay interval is divided into smaller pieces in order to obtain an equivalent switched model with multiple time-varying delays of smaller interval, which differently from other existing approaches, the maximum switching frequency is not required for stability analysis. Thus, by the use of augmented Lyapunov-Krasovskii functionals and the Finsler’s lemma, together with some relationships among state variables intentionally defined, the inherent conservatism can be progressively reduced by refining more and more the delay partition. The superiority of the proposed method is illustrated through two benchmark examples.  相似文献   

7.
This paper investigates the state estimation problem of uncertain neutral delay systems with Markovian jumping parameters. First, a novel Lyapunov–Krasovskii (L–K) functional containing the interconnected information between neutral and discrete delay is proposed. Then, based on Jensen’s integral and Wirtinger-based inequality, the obtained results are improved by relaxing the positive-definiteness restrictions on Lyapunov matrices. Third, the state estimators are designed to guarantee the asymptotic stability of the error state system. Finally, numerical examples are provided to show the effectiveness of the proposed results.  相似文献   

8.
In this paper, the stability problem of discrete-time systems with time-varying delay is considered. Some new stability criteria are derived by using a switching technique. Compared with the Lyapunov–Krasovskii functional (LKF) approach, the method used in this paper has two features. First, a switched model, which is equivalent to the original system and contains more delay information, is introduced. It means that the criteria obtained by using the LKF method can be regarded as stability criteria for the switched system under arbitrary switching. Second, when the switching signal is known, the stability problem for the switched model under constrained switching is considered and piecewise LKFs are adopted to obtain stability criteria. Since constrained switching is less conservative than arbitrary switching if the switching signal is known, one can know that the obtained results in this paper are less conservative than some existing ones. Two examples are given to illustrate the effectiveness of the obtained results.  相似文献   

9.
严顺行  姜偕富  杨性序  葛晓华 《科技通报》2011,27(2):177-181,219
考虑了区间时变时滞模糊系统的稳定性问题.利用T-S模糊模型对模糊系统进行了研究,利用线性矩阵不等式的形式给出了此类模糊系统在时滞相关意义下保守性更小的稳定性判据.由于加入了自由矩阵,所得结果保守性更小.并且给出了一个数值例子说明了所得稳定性判据的有效性.  相似文献   

10.
The asymptotic stability of linear neutral systems with a single delay is investigated in this article. Based on the characteristic equation, new algebraic criteria for the stability of the system are derived in terms of the spectral radius of corresponding modulus matrices. The significance of our new criteria is that it takes into consideration the structure information of the system matrices, thus reducing the conservatism found in the literature. Numerical examples are given to demonstrate the new stability criteria and to compare them with the previous results in the literature.  相似文献   

11.
This study is concerned with the problem of reachable set estimation for linear systems with time-varying delays and polytopic parameter uncertainties. Our target is to find an ellipsoid that contains the state trajectory of linear system as small as possible. Specifically, first, in order to utilize more information about the state variables, the RSE problem for time-delay systems is solved based on an augmented Lyapunov-Krasovskii functional. Second, by dividing the time-varying delay into two non-uniformly subintervals, more general delay-dependent stability criteria for the existence of a desired ellipsoid are derived. Third, the integral interval is decomposed in the same way to estimate the bounds of integral terms more exactly. Fourth, an optimized integral inequality is used to deal with the integral terms, which is based on distinguished Wirtinger integral inequality and Reciprocally convex combination inequality. This can be regard as a new method in the delay systems. Finally, three numerical examples are presented to demonstrate the effectiveness and merits of the theoretical results.  相似文献   

12.
This work investigates the improved stability conditions for linear systems with time-varying delays via various augmented approaches. Some augmented approaches are augmented Lyapunov-Krasovskii functionals, augmented zero equalities, and the augmented zero equality approach. At first, by constructing augmented Lyapunov-Krasovskii functionals including the state vectors which were not considered in the previous works and augmented zero equalities, a stability criterion is proposed in the forms of linear matrix inequalities. Through the proposed Lyapunov-Krasovskii functionals and an additional functional derived from the integral inequality, a slightly improved result is derived. The proposed results do not consider the increase in the computational complexity to achieve a larger delay bound. So, by applying the augmented zero equality approach, which is a method of grafting the proposed augmented zero equality proposed in Finsler Lemma, to the proposed result, an enhanced stability result was derived. Also, the computational complexity is reduced by appropriately adjusting any vector of the integral inequality utilized in the proposed criteria. By applying some numerical examples to the proposed conditions, the effectiveness and superiority of the results are confirmed.  相似文献   

13.
We propose a coding scheme for the stabilization of continuous linear scalar systems under a communication channel with finite data rate, lossy observations and network-induced delay. Owing to the network-induced delay, uncertain control input is introduced to the corresponding discrete time systems. Furthermore, since the system state is quantized to finite-bit signals and may be randomly lost in the communication, under the proposed coding scheme, the considered scalar system is described by a switched system of more than one dimension with arbitrary switchings. We derive the conditions for first moment stability of the systems, characterizing the relations on quantization cell boundaries, packet loss probabilities, and the network-induced delay. Further, we derive the condition for almost sure stability of the systems. A numerical method is proposed to search the infimum of the data rate for first moment stability under the given condition. It is shown that for the quantizer with the infimum of the data rate for first moment stability, although the quantization cells have different lengths, the matrices corresponding to these quantization cells have the same maximum eigenvalue.  相似文献   

14.
In this paper, the balanced truncation method is investigated for discrete time-delay systems. We show that the energy associated with the system controllability and observability can be characterized via the delay Lyapunov matrices, similar to the case of continuous time-delay systems. Then, we balance the system via a coordinate transformation in order to retain the delay structure of systems naturally. In this way, the balanced truncation method is conducted to obtain structure-preserving reduced models. Further, we provide an efficient process to compute a low-rank approximation to delay Lyapunov matrices based on the equivalent expression of discrete time-delay systems, which enables an approximate but fast execution of the proposed method. The stability of reduced models is also discussed in the paper. Finally, numerical examples are simulated to verify the feasibility and efficiency of the proposed method.  相似文献   

15.
This work is concerned with the problem of reachable set synthesis for a class of singular systems with time-varying delay via the adaptive event-triggered scheme. Compared with the static event-triggered mechanism, the adaptive event-triggered mechanism can save the communication resources more effectively. By virtue of Lyapunov stability theory, sufficient conditions are given to guarantee the stability of the closed-loop system and that the reachable set of the resulting system is bounded by the obtained ellipsoid. In addition, by using linear matrix inequality technique and free-weighting matrix method, the weighting matrix of event-triggered condition and proportional-derivative (P-D) feedback controller gains are obtained. The effectiveness and superiority of the developed control approach are substantiated by a numerical example and two practical examples.  相似文献   

16.
The problem of asymptotic stability of linear neutral systems with multiple delays is addressed in this article. Using the characteristic equation approach, new delay-independent stability criteria are derived in terms of the spectral radius of modulus matrices. The structure information of the system matrices are taken into consideration in the proposed stability criteria, thus the conservatism found in the literature can be significantly reduced. Simple examples are given to demonstrate the validity of the criteria proposed and to compare them with the existing ones.  相似文献   

17.
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   

18.
This paper investigates an event-triggered control design approach for discrete-time linear parameter-varying (LPV) systems under control constraints. The proposed conditions can simultaneously design a parameter-dependent dynamic output feedback controller and an event generator, ensuring the closed-loop system’s regional asymptotic stability. Based on the Lyapunov stability theory, these conditions are given in terms of linear matrix inequalities (LMIs). Moreover, using some proposed optimization procedures, it is possible to minimize the number of sensor transmissions, maximize the estimation of the region of attraction of the origin, and incorporate optimal control criteria into the formulation. Through numerical examples, some comparisons with other approaches in the literature evidence the proposed technique’s efficacy.  相似文献   

19.
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   

20.
This paper addresses the problem of quantized feedback control for networked control systems (NCSs). Firstly, with consideration of the effect of network conditions, such as network-induced delays, data packet dropouts and signal quantization, the sampled-data model of closed-loop feedback system based on the updating sequence of the event-driven holder is formulated, from which a continuous system with two additive delay components in the state is developed. Subsequently, by making use of a novel interval delay system approach, the stability analysis and control synthesis for NCSs with two/one static quantizer are solved accordingly. Finally, two illustrative examples are given to show the effectiveness and advantage of the method.  相似文献   

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