On the stability of randomly sampled systems

Randomly sampled linear systems with linear or non-linear feedback loops are studied by a stochastic Lyapunov function method. The input in this paper is assumed zero; driven systems will be treated in a later paper. Improved criteria for stability (with prebability one, on th moment , or in mean-square) are given when the sequence of holding times are independent. The method is relatively straightforward to apply, especially in comparison with the direct methods, and allows the study with nonlinear feedback or nonstationary holding times. A randomly sampled Lur\´e problem is studied. Numerical results, describing some interesting phenomena, such as, jitter stabilized systems are presented.