Analysis of Stochastic Switched Systems with Application to Networked Control Under Jamming Attacks

Abstract: We investigate the stability problem for discrete-time stochastic switched linear systems under the specific scenarios where information about the switching patterns and the probability of switches are not available. Our analysis focuses on the average number of times each mode becomes active in the long run and, in particular, utilizes their lower- and upper-bounds. This setup is motivated by cyber security issues for networked control systems in the presence of packet losses due to malicious jamming attacks where the attacker's strategy is not known a priori. We derive a sufficient condition for almost sure asymptotic stability of the switched systems which can be examined by solving a linear programming problem. Our approach exploits the dynamics of an equivalent system that describes the evolution of the switched system's state at every few steps; the stability analysis may become less conservative by increasing the step size. The computational efficiency is further enhanced by exploiting the structure in the stability analysis problem, and we introduce an alternative linear programming problem that has fewer variables. We demonstrate the efficacy of our results by analyzing networked control problems where communication channels face random packet losses as well as jamming attacks.