Output‐feedback Lyapunov redesign of uncertain systems with delayed measurements

This paper presents an output‐feedback Lyapunov redesign for uncertain systems with the delayed measurements, which recasts the state estimation and robust control into a unified framework. Instead of the traditional observer/differentiator‐based output‐feedback design, a static state estimator is constructed by the Taylor expansion of delayed measurements with the integral remainders. Then, a sliding variable is constructed according to the nominal Lyapunov function. A Lyapunov redesign approach is used to keep the system trajectory in predefined vicinity of origin, even subject to approximation errors and exogenous disturbances. The maximum value of the allowable delays for the closed‐loop stability is found via linear matrix inequalities. Finally, the effectiveness of the proposed method is verified in the magnetic suspension system.