Exponential stability of stochastic switched systems

Abstract

This paper proposes a method for exponential m-stability analysis of stochastic switched systems. The models, in a finite set of models, are non-linear stochastic models. It is assumed that there is no jump in the state at switching instants and there is no Zeno behaviour, ie, there is finite number of switches on every bounded interval. The stochastic hybrid systems have wide applications: transmission control protocol flows with congestion avoidance and slow-start modes; estimation in distributed networked systems; air traffic control; process control and communication networks for control systems. For analysis of stochastic switched system the multiple Lyapunov functions are used and exponential m-stability is proved. From the main result of the paper: 1) the exponential m1 -stability of stochastic switched systems whereby m1 ∈ (0, m); 2) the stability in probability. The exponentially stable equilibrium of system is relevant for practice because such systems are robust to perturbations.