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 H 2, H ∞ and H 2/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.

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