Exponential Stability of Discrete Time-Varying Purturbed Markov Switched Systems with Impulsive Jump

The exponential stability of a class of discrete time-varying impulsive jump linear systems with a finite-state Markov chain form process is studied. The given jump linear systems are composed of stable subsystems and unstable subsystems. Based on the average dwell time concept and by dividing the total activation time into the time with stable subsystems and the time with unstable subsystems, it is shown that if the average dwell time and the ratio of the expectation of the activation time with stable subsystems to the expectation of the activation time with unstable subsystems are properly large, the given jump linear system is exponentially stable with a desired stability margin even if there exists impulse jump at the switching instances