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Sampling-interval-dependent stability for linear sampled-data systems with non-uniform sampling. (English) Zbl 1347.93170
Summary: This paper is concerned with the sampling-interval-dependent stability of linear sampled-data systems with non-uniform sampling. A new Lyapunov-like functional is constructed to derive sampling-interval-dependent stability results. The Lyapunov-like functional has three features. First, it depends on time explicitly. Second, it may be discontinuous at the sampling instants. Third, it is not required to be positive definite between sampling instants. Moreover, the new Lyapunov-like functional can make use of the information fully of the sampled-data system, including that of both ends of the sampling interval. By making a new proposition for the Lyapunov-like functional, a sampling-interval-dependent stability criterion with reduced conservatism is derived. The new sampling-interval-dependent stability criterion is further extended to linear sampled-data systems with polytopic uncertainties. Finally, examples are given to illustrate the reduced conservatism of the stability criteria.

MSC:
93C57 Sampled-data control/observation systems
93C05 Linear systems in control theory
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C15 Control/observation systems governed by ordinary differential equations
93C41 Control/observation systems with incomplete information
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