Nonstationary H∞ dynamic output feedback control for discrete‐time Markov jump linear systems with actuator and sensor saturations

Abstract

SummaryThis paper is concerned with the nonstationary dynamic output feedback control problem for a class of discrete‐time Markov jump linear systems (MJLSs) under simultaneous consideration of actuator and sensor saturations. The so‐called nonstationary controllers dominated by two other different piecewise‐stationary Markov chains are introduced, making the designed controllers not only mode‐dependent but also dependent on other variations associated with the mode transitions in the original MJLSs. The sufficient conditions formulated in terms of bilinear matrix inequalities for the H∞ control problem are established such that the resulting closed‐loop system is stochastically stable and achieves a prescribed H∞ noise attenuation level. A suboptimal algorithm with line search is exploited to solve for the associated controller gains. Effectiveness of the developed theoretical results is verified via a numerical example. Copyright © 2015 John Wiley & Sons, Ltd.