ℋ ₂ and ℋ ∞ robust output feedback control for continuous time 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, new sufficient conditions for ℋ2 and ℋ∞ robust output feedback control synthesis are 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 ℋ2 robust control design of an inverted pendulum with uncertain friction coefficients and ℋ∞ reliable control systems design illustrate the theory.