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A refined input delay approach to sampled-data control. (English) Zbl 1205.93099

Summary: This paper considers sampled-data control of linear systems under uncertain sampling with the known upper bound on the sampling intervals. Recently a discontinuous Lyapunov function method was introduced by using impulsive system representation of the sampled-data systems [P. Naghshtabrizi, J. P. Hespanha and A. R. Teel, Syst. Control Lett. 57, No. 5, 378–385 (2008; Zbl 1140.93036)]. The latter method improved the existing results, based on the input delay approach via time-independent Lyapunov functionals. The present paper introduces novel time-dependent Lyapunov functionals in the framework of the input delay approach, which essentially improve the existing results. These Lyapunov functionals do not grow after the sampling times. For the first time, for systems with time-varying delays, the introduced Lyapunov functionals can guarantee the stability under the sampling which may be greater than the analytical upper bound on the constant delay that preserves the stability. We show also that the term of the Lyapunov function, which was introduced in the above mentioned reference for the analysis of systems with constant sampling, is applicable to systems with variable sampling.

MSC:

93C57 Sampled-data control/observation systems
93C05 Linear systems in control theory
93D30 Lyapunov and storage functions

Citations:

Zbl 1140.93036
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References:

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