A unified control design for a class of discrete-time Markov jump systems: A game approach

This study is devoted to investigating the inherent relationship among the H₂, H_∞, and H₂/H_∞ control designs for discrete-time Markov jump systems with multiplicative noise. From a new perspective of nonzero-sum Nash game, we will show that the Nash equilibrium solution may present a unified treatment approach for these three types of controller design by taking adequate parameters in the quadratic performance indices. A numerical example is also supplied to illustrate the proposed results.