Delay Dependent Robust Exponential Stability Criterion for Perturbed and Uncertain Neutral Systems with Time Varying Delays

Abstract

This paper deals with the issue of robust exponential stability of uncertain neutral system with time varying delay and nonlinear perturbations. Using Lyapunov-Krasovskii functional, new sufficient delay dependent stability conditions have been derived in terms of Linear Matrix Inequalities LMIs solved using efficient convex optimization algorithms. Neither model transformation, nor estimating techniques for cross terms, nor free weighting matrices are involved in this work. Numerical examples are considered to show the efficiency of the proposed stability approach.

A delay decomposition approach for exponential stability of perturbed neutral systems with mixed delays

“…The functions fo(t ,x(t )), fi (t ,x(t -h)) , and h (t ,x(t -T)) are unknown time varying nonlinear uncertainties. It is assumed that fi(t , 0) == 0, i == 0, 1, 2 , and: li fo I I � P o Il x(t) ll , li fi II � p ] ll x(t -h) II ' Il h II � P 2 11 x(t -T) II (2) where, for simplicity, fa :==fo(t ,x(t )), fi :==fi(t ,x(t -h)) and h :==h(t ,X(t -T)) and P i ' i==0, 1, 2 are positive scalars.…”

“…In practice, system models can be described by functional differential equation of neutral type, being a special case of time delay system which involved time delay in both state and state derivative simultaneously. Furthermore, practical systems almost present some perturbations, thus the problem of robust stability analysis has been widely investigated in many reports [2], [6], [9], [11], [12], and many approaches have been developed to solve the stability problem for neutral time-delay systems.…”

Lead-lag Controller Design for Time Delay Systems Using Genetic Algorithms

“…Time delay inherently exists in many physical systems such as chemical, mechanical and hydraulic systems [3], [22] and [24]. Therefore, it is natural that the above line of research was extended to time delay systems, see [1], [2], [8], [9], [10], [11], [13], [14], [28] and [33]. This paper aims at proposing a method to design stabilizing lead-lag controllers for time delay systems.…”

Finite-Time Convergence Stability of Lur’e Discrete-Time Systems

“…In classical control engineering [3,34], deadbeat control [13,16,29,31] is considered as an advanced control design technique, developed in the context of finite time stabilization and finite settling time, which aims to perfectly tracking a step reference in a finite number of sampling periods. In this section, we provide a methodology to design dead-beat controllers that achieve good transient performance of the linear discretetime system defined by (3) or by (6) - (7), when the nonlinearity f (ε k ) is considered constant and equal to K. The main issue to solve this problem, is how to choose the controller parameters λ i , i=0,1,… ,n−1 of the polynomial N(s) which guarantee a transient response elimination in n sampling time, where nT s constitutes the shortest possible settling time of a linear discrete-time control system for a given value of T s [31].…”