Improved stability criteria and controller design for linear neutral systems

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.