Stabilization of nonhomogenous semi-Markov jump linear systems with synchronous switching delays via aperiodically intermittent control

Abstract

A type of nonhomogenous semi-Markov jump linear systems with synchronous switching delays is considered in the present paper. Owing to the existence of time-varying delays and nonhomogenous semi-Markov switching process, the selection of Lyapunov functional and the transformation of some time-varying parameters become more complicated in comparison with many existing works. To overcome these difficulties, a sort of Lyapunov–Krasovskii functional related to switching delays is introduced. Simultaneously, the technique of convex combination is applied to tackle a variety of time-varying terms including transition probabilities (TPs), probability distribution function and probability density function (PDF). Then, a time-invariant stability criterion superior to many relevant works in conservativeness is obtained to ensure mean-square exponential stability (MES). Based on this result, time-invariant conditions for mean square exponential stability of the controlled system are also attained by the continuous feedback control. Subsequently, to stand on the point of cost reduction, an aperiodically intermittent control (AIC) is adopted in such a system and a stability criterion is attained as well under more relaxed restrictions on relative parameters. Finally, a numerical example is provided to verify the effectiveness and correctness of the results.