Lyapunov functions and gain bounds for systems with slope restricted nonlinearities

The stability and L 2 performance analysis of systems consisting of an interconnection of a linear-time-invariant (LTI) system and a static nonlinear element which is Lipschitz, slope restricted and sector bounded is revisited. The main thrust of the paper is to improve and extend an existing result in the literature to enable (i) concise and correct conditions for asymptotic stability of the interconnection and (ii) reasonably tight bounds on the L 2 gain between an exogenous input and a given output to be obtained. Numerical examples indicate that the proposed algorithm performs well compared to competing results in the literature.