A NUMERICAL ALGORITHM FOR ROBUST STABILIZATION OF SYSTEMS WITH SECTOR-BOUNDED NONLINEARITY

We consider the robust stabilization problem for systems with a nonlinear, sector-bounded uncertainty. A solution for this problem can be obtained via dynamical output feedback if a Lyapunov function of Lur'e-Postnikov type is known. Computationally, this involves the solution of an algebraic Riccati equation of H∞-type. We show how to compute the robustly stabilizing output feedback solving a generalized eigenproblem of Hamiltonian/skew-Hamiltonian structure, thereby avoiding the numerically hazardous formation of the coefficients in the algebraic Riccati equation which may lead to large errors in the computed Riccati solution and thus in the output feedback.