Delay‐dependent stability and stabilization of neutral time‐delay systems

Abstract

SUMMARYThis paper is concerned with the problem of stability and stabilization of neutral time-delay systems. A new delay-dependent stability condition is derived in terms of linear matrix inequality by constructing a new Lyapunov functional and using some integral inequalities without introducing any free-weighting matrices. On the basis of the obtained stability condition, a stabilizing method is also proposed. Using an iterative algorithm, the state feedback controller can be obtained. Numerical examples illustrate that the proposed methods are effective and lead to less conservative results.

Improved conditions for neutral delay systems with novel inequalities

“…Clearly, the results of h in [4,7,8,18] and [14] are much more conservative than those in [3,17] and Theorem 3.1. It is observed from Table 2 that our time-delay h is much bigger than existing results with the less variables.…”

Delay-dependent Robust Passivity for Uncertain Neural Networks with Time-varying Delays

“…Lemma 3 [13]. From Lemma 1, for any constant matrix ,      , the following integral inequalities can be easily obtained: …”

A New Augmented Lyapunov Functional Approach to Robust Delay-dependent Stability Analysis for Neutral Time-delay Systems

“…In this regard, bounding technique of cross terms [3], descriptor system approach [4], neutral model transformation [5], free-weighting matrix techniques [6]- [7], augmented Lyapunov functional approach [12]- [13], [16]- [17] have given major contributions in this field.…”

“…Recently, triple-integral terms in the Lyapunov -Krasovskii's functionals were introduced in [13] and showed the improvement of feasible region of delay bounds. In [13], one-integral terms were included in augmented variables.…”

“…In [13], one-integral terms were included in augmented variables. If double-integral terms are used in augmented variables, can the results be improved?…”