State-multiplicative Retarded Systems - Robust $H_{2}$ Static Output-feedback Control

The problem of robust static Linear Quadratic Regulation (LQR) problem is solved for uncertain, continuous time, retarded systems with multiplicative noise. A design solution is obtained, based on a descriptor approach, for the uncertain polytopic case where the parameters of the system matrices reside in a given polytope. The latter solution method 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 extended also to the gain-scheduling case.