Abstract
This study is concerned with the infinite horizon H 2/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 H 2/H ∞ control is presented, which transforms the design of H 2/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.
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