Transient response analysis of Lur´e systems using linear matrix inequalities

In this paper, we consider a novel approach to the initial condition response (ICR) analysis of non-linear time-varying systems of the Lur´e type. To quantify the transient behavior resulting from initial conditions, an ICR measure is defined. It is shown that an appropriate upper bound for the ICR measure can be calculated based upon the condition number of a positive definite matrix, associated with a quadratic Lyapunov function. Due to the particular structure of the Lur´e systems, bounding the ICR measure is transformed into a minimization problem, constrained by either two simultaneous Lyapunov matrix inequalities or a single algebraic Riccati inequality