Design of a resilient finite-time based unknown input observer for Lipschitz switched systems

This study introduces an extended resilient switched unknown input observer for Lipschitz nonlinear switched systems, incorporating finite-time stability concepts and multiple Lyapunov functions. The observer ensures that estimation errors remain within a predetermined bound, even when disturbances and asynchronous switching occur. By employing multiple Lyapunov functions, the observer mitigates limitations through the "jump high" condition, albeit with imposed dwell time restrictions on the switching signal. To alleviate these limitations compared to other approaches, a simultaneous design of the observer and switching signal with persistent dwell-time structure is proposed. Finite-time stability constraints, formulated as a feasibility problem using linear matrix inequalities, regulate the energy variation rate during matched intervals, mismatched intervals, and switching moments, ensuring the estimation error remains within the desired bound. A numerical simulation of a continuous stirred tank reactor system is conducted to evaluate the effectiveness of the proposed system, confirming its efficacy.