We consider the problem of zero-order output feedback control for retarded state-multiplicative stochastic systems. The delay appears in the system states where the stochastic noise multiplies both the delayed and non-delayed states. A solution is found for the nominal case where all the system matrices are fixed, resulting in a tractable LMI condition. Re-shaping the latter LMI condition to an equivalent inequality enables us to solve the robust zero-output feedback control for the uncertain polytopic case, via the application of a special version of the Finsler lemma. A solvable set of LMIs is obtained for the robust case that depends on only two tuning parameters. The presented theory is applied to a real control engineering problem taken from the field of aircraft control where the pitch control of the F4E aircraft is obtained for some special conditions.

Linear uncertain continuous-time systems with state-multiplicative noise in the presence of input delay are investigated. The stochastic uncertainty appears in the non-delayed dynamic matrix of the system and is given as a white multiplicative zero-mean real scalar Wiener process. The problem of H∞state-feedback control of these systems is solved via a predictor-based control strategy. A new stability condition is derived in a form of linear matrix inequality and is extended to a condition that guarantees a prescribed L2- gain bound for the stochastic system. The stability obtained by our approach allows for larger time delays in the system input compared to the non-predictive corresponding solution. The theoretical results are demonstrated by an example that shows the applicability of the theory to guidance control systems.