Numerical verification of equilibrium location bounds and local stability for nonlinear systems with parameter uncertainty

This paper presents a new numerical method to bound the location of the operating equilibrium of a nonlinear system subject to bounded parameter uncertainty and assure local stability. For this, sufficient conditions which guarantee the existence of an equilibrium within a bounded subset of state space for all parameter combinations and which prove that the location of this equilibrium is a continuous function of the parameters are derived. The conditions are verified numerically with reliable computing techniques that enable the numerical evaluation of functions and their derivatives on sets, yielding conservative results. A polytopic linear system that contains the linearized system dynamics at the operating equilibrium is obtained as part of the computation, and its stability is established with standard methods.