Mixed H2/H∞ control of time-varying stochastic discrete-time systems under uniform detectability

This study is concerned with the infinite horizon H₂/H_∞ control of time-varying stochastic discrete-time systems with state and disturbance dependent noise. The notion of uniform detectability for time-varying stochastic discrete-time systems is introduced, and some good properties are derived. Under uniform detectability, a necessary and sufficient condition for the existence of time-varying stochastic H₂/H_∞ control is presented, which transforms the design of H₂/H_∞ control into the solvability of coupled time-varying matrix-valued equations. Finally, an iterative algorithm is proposed to solve the coupled time-varying matrix-valued equations, and a numerical example is provided to show the effectiveness of the obtained results.