Stability analysis for nonautonomous nonlinear systems; An interval approach

One of the most important issues in control systems community is determining the stability of a system. Since the 1960’s, Lyapunov-based methods have been developed to determine the stability of linear and nonlinear systems. The main idea is finding the largest positive invariant set for a nonlinear nonautonomous system, i.e. once the system states are inside this set then it will remain inside forever. However, in general, Lyapunov based methods existing in the literature provide a pessimistic set, i.e. it contains states towards the system cannot converge and is too large to help us to find a significant limit set and do not exist a general method to find the largest invariant set. Moreover, when the system is nonlinear and uncertain (as it is the case for many existing systems), in a set-membership context, finding the largest invariant set is challenging and no reliable methods have been developed. This paper proposes an original and general set-membership based approach to find the largest positive invariant set for a nonlinear nonautonomous system with and without uncertainties.