Stability Analysis of Aperiodic Sampled-Data Systems: A Switched Polytopic System Method

Stability of aperiodic sampled-data systems is investigated in this brief. A sampling interval discretization method is proposed to transform an aperiodic sampled-data system into a discrete-time switched polytopic system with help of the convex approximation technique. Using a high order time-scheduled switched homogeneous Lyapunov function (TSSHLF), a necessary and sufficient stability condition for the discrete-time switched polytopic system is proposed and presented in terms of linear matrix inequality (LMI). On the basis of this result, a sufficient stability criterion for the aperiodic sampled-data system is obtained. Finally, numerical examples are given to confirm the effectiveness of the proposed method and significant improvements over some existing ones.

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