Technical communique: Improved stability criteria and controller design for linear neutral systems

By Qing-Long Han. 2009

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This paper is concerned with the problems of stability and H"~ control of linear neutral systems. Firstly, some new simple Lyapunov-Krasovskii functionals are constructed by uniformly dividing the discrete delay interval into multiple segments, and choosing proper functionals with different weighted matrices corresponding to different segments in the Lyapunov-Krasovskii functionals. Then using these new simple Lyapunov-Krasovskii functionals, some new delay-dependent stability criteria are derived. These criteria include some existing results as their special cases and are much less conservative than some existing results, which is shown through a numerical example. Secondly, a delay-dependent bounded real lemma (BRL) is established. Employing the obtained BRL, some delay-dependent sufficient conditions for the existence of a delayed state feedback controller, which ensure asymptotic stability and a prescribed H"~ performance level of the corresponding closed-loop system, is formulated in terms of a linear matrix inequality (LMI). A numerical example is also given to illustrate the effectiveness of the design method.

Subfields: Computational Theory and Mathematics, Computer Networks and Communications, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/cd4d19eea51b8d1319f9616ac57daab1f0f4936d