Worst Case Gain Computation of Linear Time-Varying Systems Over a Finite Horizon

Abstract

This paper presents an approach to compute the worst case gain of the interconnection of a finite time horizon linear time variant (LTV) system and a perturbation. The input/output behaviour of the uncertainty is described by integral quadratic constraints (IQC). A new algorithm to obtain an upper bound on the worst case gain based on nonlinear optimization over a parameterized Riccati differential equation is proposed. The Riccati differential equation is derived from dissipation conditions. It provides an efficient alternative to a similar approach based on solving a semidefinite program. The algorithm is applied to the atmospheric flight phase of a space launcher. A comparison to the semidefinite programming approach highlights the capabilities of this new approach.