On Robust Output Feedback Control For Polytopic Systems

Robust dynamic output feedback design is an open problem, computationally speaking, since its determination asks for the solution of nonlinear matrix inequalities, namely bilinear ones. This is particularly the case, for polytopic uncertainty. Here a new sufficient condition is proposed by the use of bounds and scaling for completion of squares. The usefulness of the provided conditions stands in the fact that its solution can be performed using the Frank-Wolfe algorithm which runs in only one shot. The control design of an inverted pendulum with uncertain friction coefficients illustrates the theory.