Robustness Analysis of Nonlinear Systems Along Uncertain Trajectories

Abstract

The paper presents a novel approach for robustness analysis of nonlinear dynamic systems in the vicinity of a reference trajectory. The approach linearizes the system with respect to a nominal trajectory and calculates a guaranteed upper bound on the worst-case gain. In contrast to existing methods rooted in linear time-varying systems analysis, the approach accurately includes perturbations that drive the system away from the reference trajectory. The approach further includes a bound for the error associated with the time-varying linearization. Hence, the results obtained in the linear framework provide a valid upper bound for the worst-case performance of the nonlinear system. The calculation of the upper bound relies on the dissipation inequalities formulated in the framework of integral quadratic constraints. It is therefore computationally much cheaper than sample-based methods such as Monte Carlo simulation. The feasibility of the approach is demonstrated on a numerical example.