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State-dependent sampling for Linear Time Invariant systems: A discrete time analysis

This work concerns the adaptation of sampling times for Linear Time Invariant (LTI) systems controlled by state feedback. Complementary to various works that guarantee stabilization independently of changes in the sampling rate, here we provide conditions to design stabilizing sequences of sampling instants. In order to reduce the number of these sampling instants, a dynamic scheduling algorithm optimizes, over a given sampling horizon, a sampling sequence depending on the system state value. Our proofs are inspired by switched system techniques combining Lyapunov functions and LMI optimization. To show the applicability of the technique, the theoretical study is illustrated by an implementation in Matlab/TRUE TIME.