Stabilization of linear systems with state dependent noise via output feedback and its application to robust control design*

The purpose of this paper is a parametrization (parametric description) of static output feedback stabililizing controllers for linear continuous-time systems with state-dependent noise. Applications of this result to robust stabilization and passification problems are considered. Algorithms for computing stabilizing gains are produced. The approach presents parametrization in terms of linear matrix equation and quadratic matrix inequalitity which depend on parameter matrices similar to weight matrices in LQR theory. To avoid implementation problems a convex approximation technique is used and LMI based algorithms are obtained for computing stabilizing gains. These algorithms are non-iterative and rely on computationally efficient LMI resolution. Yet, they are conservative but rely on a well known to use LQR methodology to choose a priori design matrices. As a result of this work a new unified approach to design of static output feedback stabilizing control is developed. Application of the obtained results to the problem of robust stabilization and passification for uncertain linear system is given.