Jiqing Qiu

Non-fragile guaranteed cost control for uncertain stochastic nonlinear time-delay systems

This paper deals with the problem of non-fragile guaranteed cost control for a class of uncertain stochastic nonlinear time-delay systems. The parametric uncertainties are assumed to be time-varying and norm bounded. The time-delay factors are unknown and time-varying with known bounds. The aim of this paper is to design a memoryless non-fragile state feedback control law such that the closed-loop system is stochastically asymptotically stable in the mean square for all admissible parameter uncertainties and the closed-loop cost function value is not more than a specified upper bound. A new sufficient condition for the existence of such controllers is presented based on the linear matrix inequality (LMI) approach. Then, a convex optimization problem is formulated to select the optimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function. Numerical example is given to illustrate the effectiveness of the developed techniques.

A novel observer-based output feedback controller design for discrete-time fuzzy systems

This paper addresses the problem of observer-based output feedback controller designs for discrete-time T-S fuzzy systems based on a relaxed approach in which the fuzzy Lyapunov functions are used. Different from the existing two-step method, a single-step linear matrix inequality method is provided for the observer-based controller design. It is shown that the controller and observer parameters can be obtained by solving a set of strict linear matrix inequalities that are numerically feasible with commercially available software. The new design method not only overcomes the drawback induced by the two-step approach but also provides less conservative results over some existing results. Finally, the effectiveness of the proposed approach is demonstrated by an example.

A new criterion for exponential stability of uncertain stochastic neural networks with mixed delays

This paper deals with the problem of exponential stability for a class of uncertain stochastic neural networks with both discrete and distributed delays (also called mixed delays). The system possesses time-varying and norm-bounded uncertainties. Based on Lyapunov-Krasovskii functional and stochastic analysis approaches, new stability criteria are presented in terms of linear matrix inequalities to guarantee the delayed neural networks to be robustly exponentially stable in the mean square for all admissible parameter uncertainties. Numerical examples are given to illustrate the effectiveness of the developed techniques.

Optimal Guaranteed Cost Control for a Class of Uncertain Systems with both State and Input Delays via Delta Operator Approach

In this paper, we investigate the optimal guaranteed cost control problem for a class of uncertain delta operator systems with both state and input delays. Based on Lyapunov-Krasovskii functional in delta domain, sufficient conditions for the existence of guaranteed cost controller of the class of delta operator systems are presented in terms of linear matrix inequalities (LMIs). The proposed method can unify some previous related continuous and discrete systems with uncertainties into the delta operator systems framework.

Delay-dependent robust H∞ control for uncertain stochastic time-delay system

This article deals with the problem of robust stabilisation and ℋ∞ control for a class of uncertain stochastic time-delay system. The parametric uncertainties are real time-varying and norm bounded. The aim is to design a memoryless state-feedback control law such that the closed-loop system are robustly stochastically asymptotically stable in the mean square and the effect of the disturbance input on the controlled output is less than a prescribed level for all admissible parameter uncertainties. New sufficient conditions for the existence of such control law are presented based on the linear matrix inequalities approach. Numerical examples are given to illustrate the effectiveness of the developed techniques.

New global asymptotic stability criterion for neural networks with discrete and distributed delays

Abstract This paper investigates the problem of global asymptotic stability for a class of neural networks with time-varying and distributed delays. By the Lyapunov-Krasovskii functional approach, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). The new stability condition does not require the time delay function to be continuously differentiable and its derivative to be less than 1, and it allows the time delay to be a fast time-varying function. Simulation examples are given to demonstrate the effectiveness of the developed techniques.

Filtering for a class of discrete-time systems with time-delays via delta operator approach

In this article, a robust H ∞ filtering problem for a class of norm-bounded uncertain discrete-time systems with time delays is investigated using delta operator approach. Based on Lyapunov–Krasovskii functional in delta domain, a new delay-dependent sufficient condition for the solvability of this problem is presented in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, an expression of a desired delta operator H ∞ filter is given. The proposed method can unify some previous related continuous and discrete systems into a delta operator systems framework. A numerical example is given to illustrate the effectiveness of the developed techniques.

Robust Stability Of Uncertain Linear Systems with Time-Varying Delay and Non-Linear Perturbations

Abstract In this paper, the problem of robust stability for uncertain linear systems with time-varying delay and non-linear perturbations is investigated. The systems possess both nonlinear perturbations and norm-bounded uncertainties. Based on the Lyapunov-Krasovskii functional approach and S procedure, a new delay-dependent stability criterion is presented, which is in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the developed techniques.

Fault Estimation for Nonlinear Dynamic Systems

In this paper, the problems of fault detection and estimation for nonlinear dynamic systems are considered by using fault detection observer and adaptive fault diagnosis observer. Based on Lyapunov stability theory and linear matrix inequality (LMI) techniques, a new sufficient condition in terms of LMIs for the proposed problem is derived. At the same time, we get the adaptive fault estimation algorithm. The LMI condition can be easily solved by MATLAB LMI toolbox. Finally, a flexible joint robotic example is given to illustrate the efficiency of the proposed approach.

Robust Stochastic Stabilization and H∞ Control for Neutral Stochastic Systems with Distributed Delays

This paper considers the problem of robust stabilization and H∞ control for a class of uncertain neutral stochastic systems, in which delay is distributed and the parametric uncertainties are norm-bounded. By designing a state feedback controller, we obtain a delay-dependent criterion such that the resulting closed-loop system is robustly stochastically asymptotically stable in the mean square and the effect of the disturbance input on the controlled output is less than a prescribed level for all admissible parameter uncertainties. New sufficient conditions are presented based on the linear matrix inequality approach. Finally, numerical examples are used to illustrate the effectiveness and feasibility of the approaches proposed in this paper.