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

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Ahmet Cetinkaya, Hideaki Ishii, Tomohisa Hayakawa

We investigate the stability problem for discrete-time stochastic switchedlinear systems under the specific scenarios where information about theswitching patterns and the probability of switches are not available. Ouranalysis focuses on the average number of times each mode becomes active in thelong run and, in particular, utilizes their lower- and upper-bounds. This setupis motivated by cyber security issues for networked control systems in thepresence of packet losses due to malicious jamming attacks where the attacker'sstrategy is not known a priori. We derive a sufficient condition for almostsure asymptotic stability of the switched systems which can be examined bysolving a linear programming problem. Our approach exploits the dynamics of anequivalent system that describes the evolution of the switched system's stateat every few steps; the stability analysis may become less conservative byincreasing the step size. The computational efficiency is further enhanced byexploiting the structure in the stability analysis problem, and we introduce analternative linear programming problem that has fewer variables. We demonstratethe efficacy of our results by analyzing networked control problems wherecommunication channels face random packet losses as well as jamming attacks.

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