Stochastic Robust Linear W-infinity Control via Dynamic Output Feedback

Abstract

This paper introduces a robust W-infinity optimal control framework for linear It\^o diffusions using a weighted Sobolev-space performance measure. Because the sample paths of It\^o diffusions are nondifferentiable, the formulation leverages the weak derivative of the expected state. An LMI-based semidefinite program is developed for dynamic output-feedback synthesis, and a rigorous stability analysis guarantees mean-square ultimate boundedness with minimized ultimate bound. A numerical example demonstrates that the proposed approach provides effective disturbance attenuation with fast transient performance.