Stochastic Zero-Sum Game and H∞ Control of Uncertain Markov Jump Systems
Considering the uncertain situation that the presence of perturbations makes the model parameters and transfer probabilities not known precisely,this paper investigates the zero-sum game problem of uncertain discrete Markov jump system.By using the method of free-connection weighting matrix,the existence conditions of control strategy and the expression of the upper bound of performance index are proposed.Firstly,with the help of the free connection weight matrix,we derive the sufficient condition for the stability of the system when no control strategy is imposed.Secondly,based on the stability criterion,combined with the relaxation inequality and the collocation method,we give the sufficiency criterion for the existence of the suboptimal saddle-point equilibrium,an explicit expression of equilibrium strategy,and a precise upper bound on the performance index.Then,by applying the theory of zero-sum game,we solve the zero-sum game problem of the uncertain stochastic Markov jump system.And stochastic H∞ control are provided as an immediate application.Finally,numerical simulation is carried out with the economic system as an example to verify the validity and practicability of the research results.
e-suboptimal saddle equilibriumuncertain system parametersgener-ally bounded transition probabilitiesH∞ control
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