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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Errata

An Erratum has been published for this content:

Corrections to ‘Mixed $H 2 / H ∞$ control of time-varying stochastic discrete-time systems under uniform detectability’

Mixed H ₂/H _∞ control of time-varying stochastic discrete-time systems under uniform detectability

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Mixed H 2/H ∞ control of time-varying stochastic discrete-time systems under uniform detectability

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Mixed H ₂/H _∞ control of time-varying stochastic discrete-time systems under uniform detectability