## Improved stability criteria and controller design for linear neutral systems.(English)Zbl 1185.93102

Summary: This paper is concerned with the problems of stability and $$H_\infty$$ 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 $$H_\infty$$ performance level of the corresponding closed-loop system, are formulated in terms of a linear matrix inequality. A numerical example is also given to illustrate the effectiveness of the design method.

### MSC:

 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93B51 Design techniques (robust design, computer-aided design, etc.) 34K40 Neutral functional-differential equations 93D20 Asymptotic stability in control theory
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### References:

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