On observer-based control of one-sided Lipschitz systems

This paper describes the novel observer-based controller design for the one-sided Lipschitz nonlinear systems. An observer-based controller design condition is obtained by application of the Lyapunov theory, by involving the one-sided Lipschitz condition and quadratic inner-boundedness criterion, and by incorporating the matrix inequality procedures. Further, a decoupling condition, necessary and sufficient for the main design approach, is developed to determine the controller and observer gains. Furthermore, two design conditions, a computationally simple sufficient condition and a more generic necessary and sufficient condition, based on the existing and the novel treatments for the one-sided Lipchitz nonlinearity are evaluated to obtain the observer-based control solution. An algorithm for solving the proposed design constraints by combining a nested bilinear-terms-solver approach and a nonlinear-optimization-based cone complementary linearization method is provided. The effectiveness of the proposed observer-based controller design for the one-sided Lipschitz nonlinear systems is demonstrated using a numerical example.