Stability analysis and stabilization of aperiodic sampled-data systems based on a switched system approach

This paper investigates the stability analysis and controller design problems for aperiodic sampled-data control systems. The time-varying sampling period is assumed to take only a finite number of values, and the considered system is modeled as a discrete-time switched system with both stable and unstable subsystems. A sufficient condition is derived for the system to be exponentially stable, and a state feedback stabilizing controller is designed such that the system is exponentially stable and achieves an optimal guaranteed cost performance. The obtained exponential decay rate and guaranteed cost performance level critically depend on both the lengths and activation frequencies of the varying sampling periods, and it is revealed that nonuniformly sampled control systems can remain to be stable even in the appearance of a very large sampling period, provided that the activation frequency of the large sampling period is small enough. Finally, an illustrative example is given to show the effectiveness of the proposed approach.