Sampled‐data exponential stabilization of switched nonlinear delayed systems with asynchronous switching

Abstract

SummaryIn this article, the exponential stabilization for a class of switched nonlinear delayed systems is addressed via aperiodic sampled‐data control with asynchronous switching. A new type of looped multiple Lyapunov‐Krasovskii functionals (LKFs) is developed, which depend both on the system modes and on the controller modes. Moreover, the constructed looped LKFs are discontinuous and relax restrictions on positive definiteness that is only required at the sampling instants and at the switching instants of system modes. Based on the looped multiple LKFs, the average dwell time approach, and some estimation techniques, a less conservative stability criterion is derived to ensure the exponential stability of the closed‐loop system. Furthermore, by decoupling the matrix inequalities in the stability criterion, a LMI‐based design algorithm for the control gains is developed, which gets further refined and becomes more flexible due to the introduction of the two adjustable parameters. Two simulation examples are finally provided to validate the effectiveness and superiority of the proposed functionals and the obtained results over some existing ones.