一类不确定线性时滞系统的输出反馈鲁棒镇定

研究一类不确定线性时滞系统的输出反馈鲁棒镇定问题,其中不确定性不必满足匹配条件。以二次Lyapunov泛函保证系统的渐近稳定性,利用线性矩阵不等式给出了系统可以利用动态输出反馈鲁棒镇定的充分条件。当此条件成立时,基于线性矩阵不等式的解构造了全阶动态输出反馈镇定控制器。     

Improved results on stability and stabilization criteria for uncertain linear systems with time-varying delays

In this paper, the problems of stability and stabilization for linear systems with time-varying delays and norm-bounded parameter uncertainties are considered. By constructing augmented Lyapunov functionals and utilizing auxiliary function-based integral inequalities, improved delay-dependent stability and stabilization criteria for guaranteeing the asymptotic stability of the system are proposed with the framework of linear matrix inequalities. Four numerical examples are included to show that the proposed results can reduce the conservatism of stability and stabilization criteria by comparing maximum delay bounds.     

Delay-dependent robust stabilization for a class of neutral systems with nonlinear perturbations

This note deals with the problem of stabilization/stability for neutral systems with nonlinear perturbations. A new stabilization/stability scheme is presented. Using improved Lyapunov functionals, less conservative stabilization/stability conditions are derived for such systems based on linear matrix inequalities (LMI). Numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.     

Delay-dependent robust stabilization for a class of neutral systems with nonlinear perturbations

This note deals with the problem of stabilization/stability for neutral systems with nonlinear perturbations. A new stabilization/stability scheme is presented. Using improved Lyapunov functionals, less conservative stabilization/stability conditions are derived for such systems based on linear matrix inequalities （LMI）. Numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.     

T-S 模糊时滞模型的时滞相关稳定性分析和镇定

研究一类用T—S模糊模型描述的非线性不确定时滞系统的时滞相关鲁棒镇定问题．基于线性矩阵不等式的可行解，首先给出利用T—S模糊模型描述的非线性时滞系统时滞相关稳定性准则；然后给出了经状态反馈鲁棒镇定设计的新方法．所设计的控制器能确保闭环系统渐近稳定．     

T-S模糊时滞系统的时滞相关镇定

基于T-S模糊模型方法,研究一类非线性区间时滞系统的稳定性分析与镇定问题,基于一组线性矩阵不等式的可解性,给出了非线性时滞系统时滞相关稳定和镇定的充分条件,并通过构造新的模糊权依赖型Lyapunov泛函,降低了稳定性准则的保守性,最后通过仿真例子表明了所提方法的有效性.     

Stability and stabilization of nonlinear discrete‐time stochastic systems

This paper mainly studies the locally/globally asymptotic stability and stabilization in probability for nonlinear discrete‐time stochastic systems. Firstly, for more general stochastic difference systems, two very useful results on locally and globally asymptotic stability in probability are obtained, which can be viewed as the discrete versions of continuous‐time Itô systems. Then, for a class of quasi‐linear discrete‐time stochastic control systems, both state‐ and output‐feedback asymptotic stabilization are studied, for which, sufficient conditions are presented in terms of linear matrix inequalities. Two simulation examples are given to illustrate the effectiveness of our main results.     

Analysis and synthesis of nonlinear time-delay systems via fuzzycontrol approach

Takagi-Sugeno (TS) fuzzy models (1985, 1992) can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input/output (I/O) submodels. In this paper, the TS fuzzy model approach is extended to the stability analysis and control design for both continuous and discrete-time nonlinear systems with time delay. The TS fuzzy models with time delay are presented and the stability conditions are derived using Lyapunov-Krasovskii approach. We also present a stabilization approach for nonlinear time-delay systems through fuzzy state feedback and fuzzy observer-based controller. Sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain are derived through the numerical solution of a set of coupled linear matrix inequalities. An illustrative example based on the CSTR model is given to design a fuzzy controller     

离散时滞切换系统的无记忆状态反馈镇定

针对一类子系统为离散时滞系统的切换系统，研究了稳定性与无记忆状态反馈镇定问题．采用多李雅普诺夫函数法，首先以线性矩阵不等式形式给出了在任意切换信号作用下离散时滞切换系统渐进稳定的一个充分性条件；然后给出了系统无记忆状态反馈镇定的控制器设计方案，并将结果推广到不确定离散时滞切换系统；最后用仿真算例验证了所提出设计方案的可行性。     

Fractional‐order–dependent global stability analysis and observer‐based synthesis for a class of nonlinear fractional‐order systems

This paper focuses on proposing novel conditions for stability analysis and stabilization of the class of nonlinear fractional‐order systems. First, by considering the class of nonlinear fractional‐order systems as a feedback interconnection system and applying small‐gain theorem, a condition is proposed for L₂‐norm boundedness of the solutions of these systems. Then, by using the Mittag‐Leffler function properties, we show that satisfaction of the proposed condition proves the global asymptotic stability of the class of nonlinear fractional‐order systems with fractional order lying in (0.5, 1) or (1.5, 2). Unlike the Lyapunov‐based methods for stability analysis of fractional‐order systems, the new condition depends on the fractional order of the system. Moreover, it is related to the H_∞‐norm of the linear part of the system and it can be transformed to linear matrix inequalities (LMIs) using fractional‐order bounded‐real lemma. Furthermore, the proposed stability analysis method is extended to the state‐feedback and observer‐based controller design for the class of nonlinear fractional‐order systems based on solving some LMIs. In the observer‐based stabilization problem, we prove that the separation principle holds using our method and one can find the observer gain and pseudostate‐feedback gain in two separate steps. Finally, three numerical examples are provided to demonstrate the advantage of the novel proposed conditions with the previous results.     

非线性滞后It(?)随机系统的滞后无关均方渐近稳定性

研究非线性滞后Ito随机系统的滞后无关均方渐近稳定性,将关于线性时滞不等式的Halanay不等式推广到非线性情形,用Lyapunov函数和关于时滞随机系统的比较原理,得到了非线性滞后Ito随机系统滞后无关均方渐近稳定性的一些判据。     

Stability of nonlinear 2D systems described by the continuous-time Roesser model

This paper considers systems with two-dimensional dynamics (2D systems) described by the continuous-time nonlinear state-space Roesser model. The sufficient conditions of exponential stability in terms of vector Lyapunov functions are established. These conditions are then applied to analysis of the absolute stability of a certain class of systems comprising a linear continuous-time plant in the form of the Roesser model with a nonlinear characteristic in the feedback loop, which satisfies quadratic constraints. The absolute stability conditions are reduced to computable expressions in the form of linear matrix inequalities. The obtained results are extended to the class of continuous-time systems governed by the Roesser model with Markovian switching. The problems of absolute stability and stabilization via state- and output-feedback are solved for linear systems of the above class. The solution procedures for these problems are in the form of algorithms based on linear matrix inequalities.     

Quadratic stability and stabilization of uncertain linear discrete-time systems with state delay

This paper deals with the problem of quadratic stability analysis and quadratic stabilization for uncertain linear discrete-time systems with state delay. The system under consideration involves state time delay and time-varying norm-bounded parameter uncertainties appearing in all the matrices of the state-space model. Necessary and sufficient conditions for quadratic stability and quadratic stabilization are presented in terms of certain matrix inequalities, respectively. A robustly stabilizing state feedback controller can be constructed by using the corresponding feasible solution of the matrix inequalities. Two examples are presented to demonstrate the effectiveness of the proposed approach.     

基于观测器的参数不确定非线性系统的模糊鲁棒控制

对一类非线性系统进行模糊建模及其模糊观测器设计, 研究了在系统的状态不可测且存在参数不确定的模糊鲁棒控制问题, 以线性矩阵不等式的形式给出了模糊控制系统具有李雅普诺夫意义下稳定的充分条件, 最后把所提出的方法应用到倒立摆系统进行仿真, 仿真结果验证了该控制方法的有效性.     

基于观测器的参数不确定非线性系统的模糊鲁棒控制

对一类非线性系统进行模糊建模及其模糊观测器设计，研究了在系统的状态不可测且存在参数不确定的模糊鲁捧控制问题，以线性矩阵不等式的形式给出了模糊控制系统具有李雅普诺夫意义下稳定的充分条件，最后把所提出的方法应用到倒立摆系统进行仿真，仿真结果验证了该控制方法的有效性。     

Delay‐dependent robust control for singular discrete‐time Markovian jump systems with time‐varying delay

The problem of delay‐dependent robust stabilization for uncertain singular discrete‐time systems with Markovian jumping parameters and time‐varying delay is investigated. In terms of free‐weighting‐matrix approach and linear matrix inequalities, a delay‐dependent condition is presented to ensure a singular discrete‐time system to be regular, causal and stochastically stable based on which the stability analysis and robust stabilization problem are studied. An explicit expression for the desired state‐feedback controller is also given. Some numerical examples are provided to demonstrate the effectiveness of the proposed approach. Copyright © 2009 John Wiley & Sons, Ltd.     

Synthesis of non-rational controllers for linear delay systems

This paper addresses the control of linear delay systems using non-rational controllers. The structure of the controller is chosen so as to copy the structure of the plant, reproducing the delays in the state and in the output. The resulting stabilization and performance design problems are entirely expressed as linear matrix inequalities. Although the design inequalities are based on delay independent stability conditions, the overall design is delay dependent, in the sense that the controller makes use of the delay parameter of the plant. This parameter is assumed to be constant yet arbitrary. Using non-rational controllers we overcome the main difficulty faced when designing rational controllers for linear delay systems, which is to incorporate in the design problem the matrix multiplier used to prove stability with respect to the delayed part of the system. We illustrate the paper with several examples and provide extensive comparisons with existent results.     

Robust Finite‐Time Stability and Stabilization of Linear Uncertain Time‐Delay Systems

Robust finite‐time stability and stabilization problems for a class of linear uncertain time‐delay systems are studied. The concept of finite‐time stability is extended to linear uncertain time‐delay systems. Based on the Lyapunov method and properties of matrix inequalities, a sufficient condition that ensures finite‐time stability of linear uncertain time‐delay systems is given. By virtue of the results on finite‐time stability, a memoryless state feedback controller that guarantees that the closed‐loop system is finite time stable, is proposed. The controller design problem is solved by using the linear matrix inequalities and the cone complementarity linearization iterative algorithm. Numerical examples verify the efficiency of the proposed methods.     

On delay-dependent stability for vector nonlinear stochastic delay-difference equations with Volterra diffusion term

Global asymptotic stability conditions for discrete vector nonlinear stochastic systems with state delay and Volterra diffusion term are obtained based on the convergence theorem for semimartingale inequalities, without assuming the Lipschitz conditions for nonlinear drift functions. The derived stability conditions are directly expressed in terms of the system coefficients. A number of nontrivial examples of nonlinear systems satisfying the obtained stability conditions are given. The obtained results are compared to some previously known asymptotic stability conditions for discrete nonlinear stochastic systems.     

Stability Analysis and Stabilization for Discrete-Time Fuzzy Systems With Time-Varying Delay

This paper is concerned with the problems of stability analysis and stabilization for discrete-time Takagi–Sugeno fuzzy systems with time-varying state delay. By constructing a new fuzzy Lyapunov function and by making use of novel techniques, an improved delay-dependent stability condition is obtained, which is dependent on the lower and upper delay bounds. The merit of the proposed stability condition lies in its reduced conservatism, which is achieved by avoiding the utilization of some bounding inequalities for the cross products between two vectors. Then, a delay-dependent stabilization approach based on a parallel distributed compensation scheme is developed for both state feedback and observer-based output feedback cases. The proposed stability and stabilization conditions are formulated in terms of linear matrix inequalities, which can be solved efficiently by using existing optimization techniques. Two illustrative examples are provided to demonstrate the effectiveness of the results proposed in this paper.