Baoyong Zhang

Filtering of Markovian Jump Delay Systems Based on a New Performance Index

This paper is concerned with the design of mode-dependent and mode-independent filters for continuous-time linear Markovian jump systems (MJSs) with time-varying delays. Different from the existing studies in the literature, the purpose of this paper is to solve the H∞, L2 - L∞ passive and dissipative filtering problems in a unified framework. This purpose is successfully realized by using a new performance index that is referred to as extended dissipativity. The extended dissipative inequality contains several weighting matrices. By tuning the weighting matrices, the extended dissipativity will reduce to the H∞ performance, L2 - L∞ performance, passivity and dissipativity, respectively. Delay-dependent conditions for the analysis of stochastic stability and extended dissipativity for MJSs with time-varying delays are obtained by using a mode-dependent Lyapunov-Krasovskii functional together with a novel integral inequality. Based on these conditions, the design methods for mode-dependent and mode-independent filters are developed based on linear matrix inequalities. The designed filters guarantee that the resulting filtering error system is stochastically stable and extended dissipative for any admissible delays. Finally, the effectiveness of the proposed methods is substantiated with three illustrative examples.

Technical communique: Improved stability criterion and its applications in delayed controller design for discrete-time systems

This paper is concerned with the problem of delay-dependent stability analysis for discrete-time systems with interval-like time-varying delays and the problem of stabilization for discrete-time linear systems via time-delayed controllers. The first problem is solved by applying a novel Lyapunov functional, and an improved delay-dependent stability criterion is obtained in terms of a linear matrix inequality. Based on this, a sufficient condition for the solvability of the second problem is presented. The reduced conservatism of the proposed stability result is shown through a numerical example, while the applicability of the time-delayed controller design method is demonstrated by an inverted pendulum system.

Improved delay-dependent exponential stability criteria for discrete-time recurrent neural networks with time-varying delays

This paper is concerned with the problem of stability analysis for a class of discrete-time recurrent neural networks with time-varying delays. Under a weak assumption on the activation functions and using a new Lyapunov functional, a delay-dependent condition guaranteeing the global exponential stability of the concerned neural network is obtained in terms of a linear matrix inequality. It is shown that this stability condition is less conservative than some previous ones in the literature. When norm-bounded parameter uncertainties appear in a delayed discrete-time recurrent neural network, a delay-dependent robust exponential stability criterion is also presented. Numerical examples are provided to demonstrate the effectiveness of the proposed method.

Delay-Dependent Exponential Stability for Uncertain Stochastic Hopfield Neural Networks With Time-Varying Delays

This paper provides new delay-dependent conditions that guarantee the robust exponential stability of stochastic Hopfield type neural networks with time-varying delays and parameter uncertainties. Both the cases of the time-varying delays which are differentiable and may not be differentiable are considered. The stability conditions are derived by using the recently developed free-weighting matrices technique and expressed in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness of the proposed stability criteria. It is shown that the proposed stability results are less conservative than some previous ones in the literature.

Delay-dependent stabilization for stochastic fuzzy systems with time delays

This paper is concerned with the delay-dependent stabilization problem for a class of time-delay stochastic fuzzy systems. The time delays are assumed to appear in both the state and the control input. The purpose is the design of a state-feedback fuzzy controller such that the resulting closed-loop system is asymptotically stable in the mean square. A delay-dependent condition for the solvability of this problem is obtained in terms of relaxed linear matrix inequalities (LMIs). By solving these LMIs, a desired controller can be obtained. Finally, a numerical example is given to demonstrate the effectiveness of the present results.

Stability Analysis of Distributed Delay Neural Networks Based on Relaxed Lyapunov–Krasovskii Functionals

This paper revisits the problem of asymptotic stability analysis for neural networks with distributed delays. The distributed delays are assumed to be constant and prescribed. Since a positive-definite quadratic functional does not necessarily require all the involved symmetric matrices to be positive definite, it is important for constructing relaxed Lyapunov-Krasovskii functionals, which generally lead to less conservative stability criteria. Based on this fact and using two kinds of integral inequalities, a new delay-dependent condition is obtained, which ensures that the distributed delay neural network under consideration is globally asymptotically stable. This stability criterion is then improved by applying the delay partitioning technique. Two numerical examples are provided to demonstrate the advantage of the presented stability criteria.

Exact tracking control of nonlinear systems with time delays and dead-zone input

This paper is concerned with the control design problem for a class of nonlinear systems with the state time-varying time delays and nonsymmetric dead zone. The problem addressed is to design adaptive controllers that guarantee the exact tracking of a given reference signal. Two continuous robust adaptive control schemes are proposed. A positive nonlinear control gain function, which is not required to satisfy an inequality but is expressed explicitly, is carefully constructed and is used in the control law and adaptive law. An illustrative example is provided to demonstrate the validity of the proposed design method.

Robust stabilization of uncertain T--S fuzzy time-delay systems with exponential estimates

This paper deals with the problem of robust stabilization for uncertain Takagi-Sugeno (T-S) fuzzy systems with constant time delays. The purpose is to design a state-feedback fuzzy controller such that the closed-loop system is robustly exponentially stable with a prescribed decay rate. Sufficient conditions for the solvability of this problem are presented in terms of linear matrix inequalities (LMIs). By using feasible solutions of these LMIs, desired fuzzy controllers are designed and their corresponding exponential estimates are given. In addition, the main results of this paper are explicitly dependent on the decay rate. This enables one to design fuzzy controllers by freely selecting decay rates according to different practical conditions. Two numerical examples are provided finally to demonstrate the effectiveness of the proposed design methods.

Passivity analysis and passive control of fuzzy systems with time-varying delays

This paper is concerned with the passive controller design problem for a class of continuous-time Takagi-Sugeno (T-S) fuzzy systems with both state and input delays. The delays are assumed to be time-varying and differentiable. A notion of very-strict passivity is adopted. The purpose is to design a state-feedback fuzzy controller such that the resulting closed-loop system is very-strictly passive (VSP). Delay-dependent conditions for the solvability of the addressed problem are obtained by applying recently developed techniques for time-delay systems and fuzzy systems. These conditions are expressed by means of strict linear matrix inequalities (LMIs) that can be easily solved. A numerical example and simulation results are provided to demonstrate the effectiveness of the proposed method.

Relaxed passivity conditions for neural networks with time-varying delays

This paper revisits the problem of passivity analysis for neural networks with time-varying delays. A new delay-dependent criterion is obtained in terms of linear matrix inequalities, guaranteeing that the input and output of the considered neural network satisfy a prescribed passivity-inequality constraint. This newly presented criterion does not require all the symmetric matrices involved in the employed quadratic Lyapunov-Krasovskii functional to be positive definite. This feature is remarkable since it sheds new light on the traditional ideas for constructing Lyapunov-Krasovskii functionals. More importantly, the conservatism of delay-dependent passivity conditions can be reduced due to the relaxation on the positive-definiteness of every Lyapunov matrix. It is shown both theoretically and numerically that the passivity criterion proposed in this paper is truly less conservative than some of the latest results in the literature.