Computing Worst-Case Disturbances for Finite-Horizon Linear Time-Varying Approximations of Uncertain Systems

A method is presented for computing the worst-case disturbance of a given norm for a finite-horizon linear time-varying system with a nonzero initial condition. This method is motivated by the linearized robustness analysis of a nonlinear system about a finite-horizon nominal trajectory. The system is linearized about this trajectory and interconnected with sampled model uncertainties. An additional input term to improve the fidelity of the linear interconnection is introduced and is absorbed into an augmented system with a nonzero initial condition. The method, which analyzes the robustness of the resulting interconnection to disturbance, is demonstrated on the numerical example of a two-link robot arm.