Reachable set estimation for Markov jump LPV systems with time delays

Abstract This paper investigates the reachable set estimation problem for discrete-time Markov jump LPV systems with time-varying delays and bounded disturbance. The main consideration is that under zero initial conditions, how to obtain a bound set as small as possible that includes system states. Based on this, by applying a novel summation inequality integrated with the reciprocally convex approach under the framework of the Lyapunov functional method, the delay-dependent conditions are provided to guarantee the presence of an ellipsoid that bounds the system state in the existence of bounded disturbances. Some derived conditions expressed by linear matrix inequalities can be solved via utilizing different computational tools, and the minimum possible ellipsoidal bound can also be determined. Additionally, the obtained results are extensively used in the case with partially known transition probability, and some conditions with more universality are derived. Finally, a numerical example is given to illustrate the effectiveness of the results.

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