Globally exponential stabilization of a class of uncertain time delay systems via periodically intermittent control

Abstract

The problem of periodically intermittent stabilization of a class of uncertain time‐delay systems is investigated. Two cases of time‐varying delays are considered: the fast‐varying delays and the slowly‐varying delays. For the former case, a piecewise exponential‐type Lyapunov function combined with a novel Razumikhin‐type technique is proposed to analyze the stability of the periodically intermittently controlled systems. For the latter case, the stability analysis is performed by employing a piecewise time‐dependent exponential‐type Lyapunov functional. The exponential‐type Lyapunov functions/functionals are able to capture more information on switching modes than the conventional Lyapunov functions/functionals, and thus lead to less conservative stability criteria. Next, based on the newly established stability criteria, novel sufficient conditions on the existence of periodically intermittent feedback controllers are presented in terms of linear matrix inequalities. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed results.