Stability and Stabilization for Sampled-data Systems with Probabilistic Sampling

In this paper, the problems of exponential stability analysis and stabilization are investigated for sampled-data systems with probabilistic sampling. By introducing a stochastic variable satisfying a Bernoulli distribution, the probabilistic sampling system is transformed into a continuous time-delay system with stochastic parameters. A Lyapunov functional approach is developed to establish the mean-square exponential stability of the closed-loop system. Based on this, the design procedure for stabilization controllers is proposed by means of linear matrix inequalities (LMIs), which can be solved efficiently by available software. Finally, an example is given to demonstrate the effectiveness of the proposed controller design methodology.