Finite‐Time H∞ Control for a Class of Discrete‐Time Markov Jump Systems with Actuator Saturation via Dynamic Antiwindup Design

We deal with the finite‐time control problem for discrete‐time Markov jump systems subject to saturating actuators. A finite‐state Markovian process is given to govern the transition of the jumping parameters. A controller designed for unconstrained systems combined with a dynamic antiwindup compensator is given to guarantee that the resulting system is mean‐square locally asymptotically finite‐time stabilizable. The proposed conditions allow us to find dynamic anti‐windup compensator which stabilize the closed‐loop systems in the finite‐time sense. All these conditions can be expressed in the form of linear matrix inequalities and therefore are numerically tractable, as shown in the example included in the paper.