Robust Output-Feedback Stabilization: Deterministic and Stochastic Perspectives

Three parallel gaps in feedback control theory are examined: sufficiency versus necessity, deterministic versus stochastic modelling, and guaranteed robustness versus performance. Two static output-feedback control problems are considered. The Deterministic Robust Stabilization Problem involves bounded but unknown measurable time-varying parameter variations, while the Stochastic Optimal Control Problem features state- and control-dependent white noise. A general sufficiency condition for the deterministic problem is obtained using Lyapunov´s direct method, and necessary conditions for the stochastic problem are derived as a consequence of minimizing a quadratic cost criterion. The sufficiency test is then applied to the necessary condition to determine when solutions of the stochastic problem also solve the deterministic problem. As an additional application of the deterministic result, the modified Riccati equation of Petersen and Hollot is generalized.