H∞ Observer‐Based Control for a Class of One‐Sided Lipschitz Uncertain Systems in Finite Frequency Domain

ABSTRACT This paper presents a robust observer‐based control design for one‐sided Lipschitz non‐linear systems with finite frequency specifications. The objective is to co‐design the observer and controller matrices to achieve asymptotic stability and disturbance attenuation within a specified finite frequency domain, encompassing low, middle, or high frequencies. The proposed approach leverages Finsler's lemma and Parseval's theorem to develop novel sufficient conditions expressed as Linear Matrix Inequalities (LMIs). These conditions ensure effective disturbance rejection in the specified frequency ranges. Notably, the computational approach employs a decoupling technique to linearize the bilinear terms, avoiding the need for additional assumptions on system matrices, and making the bilinear matrix inequalities (BMIs) conditions solvable with standard LMI tools. Two examples illustrate the effectiveness of the suggested control scheme.