A game-based control design for discrete-time Markov jump systems with multiplicative noise

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 non-zero-sum Nash game, we show that the Nash equilibrium solution may present a unified treatment approach for these three types of control design problems by taking adequate parameters in the quadratic performance indices. Moreover, a numerical example is supplied to illustrate the proposed results.