Robust Static Output-Feedback Control of Stochastic Continuous Time-Delayed Systems

Abstract

In this article, a descriptor method is introduced for designing static output-feedback controllers for linear, continuous-time, retarded, stochastic systems that achieves a prescribed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty } {\kern2.84526pt}$</tex-math></inline-formula> performance. A design solution is obtained for the uncertain case, where the parameters of the system matrices reside in a given polytope. The latter solution enables the derivation of the required constant output gain by solving a set of linear matrix inequalities that correspond to the vertices of the uncertainty polytope. The theory developed is also extended to the gain-scheduling case, and it is demonstrated by two examples. The first example compares various solution methods and the second is one of robust pitch control of an aircraft.