Abstract
This paper addresses the multi-rate stabilization problem for linear singularly perturbed systems. The proposed multi-rate sampled-data control law is based on the discretization in multi-rate fashion on the continuous-time composite control law obtained from the singular perturbation theory. The sampling times of the slow and fast state variables are allowed to be asynchronous and nonuniformly spaced. A new time-dependent Lyapunov functional is introduced to analyze the closed-loop stability of the considered system with the multi-rate feedback. With the use of the Lyapunov functional, a sufficient condition for exponential stability of the closed-loop system is derived in terms of linear matrix inequalities. Further, a robust stabilizability condition of the proposed multi-rate control law with respect to uncertain singular perturbation parameter is also obtained. Three numerical examples are presented to show the effectiveness of the developed methodology.
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