Relationship Between Nash Equilibrium Strategies and $H_{2}/H_{\infty}$ Control of Stochastic Markov Jump Systems With Multiplicative Noise

This technical note is concerned with discussing the relationship between Nash equilibrium strategies and the finite horizon H
₂
/H
_∞
control of time-varying stochastic systems subject to Markov jump parameters and multiplicative noise. It is revealed that the equivalence of these two problems depends on whether the disturbance enters into the diffusion term. Furthermore, necessary and sufficient conditions for the finite horizon H
₂
/H
_∞
control of stochastic Markov jump systems are presented via coupled matrix-valued equations.