Gain Scheduled H ∞ and H 2 static output feedback control of discrete-time stochastic delayed systems

This paper addresses the problem of 𝐻∞ zero-order output-feedback control of state-delayed, discrete-time, state-multiplicative retarded linear systems with white noise signals multiplying both the delayed and non-delayed states of the system and the input signal. Based on the Bounded Real lemma (BRL) of these systems, a simple Linear Matrix Inequality (LMI) condition is obtained for the nominal case. The same condition is reshaped to solve the control problem for systems with polytopic-type uncertainties. The paper also addresses the stochastic 𝐻2 counterpart of the 𝐻∞ control problem for both nominal and uncertain polytopic cases. The approach proposed in the paper offers a simple and efficient solution to the 𝐻∞ and 𝐻2 control problems, especially for systems with uncertainties, and is expected to have practical applications in control engineering. The paper includes a numerical example that demonstrates the results of the various solution methods in this study.