Gain Scheduled H_∞ and H₂ static output feedback control of discrete-time stochastic delayed systems

This paper addresses the problem of (Formula presented.) 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 (Formula presented.) counterpart of the (Formula presented.) control problem for both nominal and uncertain polytopic cases. The approach proposed in the paper offers a simple and efficient solution to the (Formula presented.) and (Formula presented.) 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.