Delay-dependent Linear Matrix Inequality Condition Research Articles

Gain‐scheduled control for discrete‐time non‐linear parameter‐varying systems with time‐varying delays

This study addresses the gain-scheduled control problem for discrete-time delayed non-linear parameter-varying (NLPV) and linear parameter-varying (LPV) systems. First, by constructing the parameter-dependent Lyapunov–Krasovskii functional and employing multiple auxiliary functions, delay-dependent reciprocally convex inequality, and selecting a suitable augmented vector, novel delay-dependent linear matrix inequality conditions for the static output-feedback control design and state-feedback control design for delayed NLPV are provided. Second, the results obtained for discrete-time delayed NLPV systems are modified in a simple way to deal with discrete-time delayed LPV systems. Finally, the effectiveness of the proposed methods is illustrated by numerical examples.

Robust exponential stability and memory state feedback control for uncertain singular time‐delay systems with saturating actuators

This study is concerned with delay-dependent H ∞ robust exponential stability and memory state feedback stabilisation of singular time-delay systems with saturating actuators. First, a delay-dependent linear matrix inequality condition is obtained, which guarantees that the uncertain singular time-delay systems subject to actuator saturation are not only robustly exponential admissible, but also satisfy H ∞ performance γ via a tighter integral inequality and the method of free-weighting matrices. Then, using the conditions, the estimation of stability region and the controller with memory state feedback are given by solving a convex optimisation problem. Finally, some numerical examples are provided to demonstrate the merit of the obtained results.

Robust stability and stabilization of discrete singular systems with interval time-varying delay and linear fractional uncertainty

The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality (LMI) approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.

Stability of uncertain piecewise affine systems with time delay: delay-dependent Lyapunov approach

This article addresses the problem of robust stability of piecewise affine (PWA) uncertain systems with unknown time-varying delay in the state. It is assumed that the uncertainty is norm bounded and that upper bounds on the state delay and its rate of change are available. A set of linear matrix inequalities (LMIs) is derived providing sufficient conditions for the stability of the system. These conditions depend on the upper bound of the delay. The main contributions of the article are as follows. First, new delay-dependent LMI conditions are derived for the stability of PWA time-delay systems. Second, the stability conditions are extended to the case of uncertain PWA time delay systems. Numerical examples are presented to show the effectiveness of the approach.

Delay-dependent robust stability and stabilisation for uncertain discrete singular systems with time-varying delays

The robust stability and robust stabilisation problems for time-varying delay discrete singular systems with parameter uncertainties are discussed. A delay-dependent linear matrix inequality (LMI) condition to enable time-varying delay discrete standard state-space systems to be stable is given. Based on this condition and the restricted system equivalent transformation, the delay-dependent LMI condition is proposed for the time-varying delay discrete singular systems to be admissible. With this condition, the problems of robust stability and robust stabilisation are solved, and the delay-dependent LMI conditions are obtained. Numerical examples illustrate the effectiveness of the proposed method.

Further results on delay-dependent robust stability conditions of uncertain neutral systems

This paper deals with the problem of robust stability analysis for uncertain neutral systems. In terms of a linear matrix inequality (LMI), an improved delay-dependent asymptotic stability criterion is developed without using bounding techniques on the related cross product terms. Based on this, a new delay-dependent LMI condition for robust stability is obtained. 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. Copyright © 2005 John Wiley & Sons, Ltd.