Nonzero-sum Stochastic Differential Gamefor Discrete-Time Markovian jump Linearsystem with incomplete transition rates

Abstract

This paper investigates the guaranteed cost control problem and guaranteesthe cost Nash equilibrium for discrete-time Markovian jump Linearsystem (MJLS) with incomplete transition rates. By employing matrixinequalities and the free-connection weighting matrix approach, severalsufficient conditions are proposed to ensure the applicability of theguaranteed cost control strategy. Moreover, we provide sufficient conditionsto highlight further the correctness and lower conservativeness ofthe utilized theorems. Ensuring these conditions for the existence of aguaranteed cost Nash equilibrium affords to transform them into an optimizationproblem that simultaneously satisfies a set of BMI and matrixinequalities. Furthermore, to make the results more general, this paperdesigns guaranteed cost Nash equilibrium strategies for multiple players.Finally, two detailed numerical examples validate the paper’s theorems.