Finite Horizon Robustness Analysis of LTV Systems Using Integral Quadratic Constraints
It addresses the need for finite-horizon robustness metrics in LTV systems, which is important for applications like aerospace and control where transient behavior matters.
This paper develops a framework for finite-horizon robustness analysis of uncertain linear time-varying (LTV) systems using integral quadratic constraints (IQCs), providing sufficient conditions for computing robust induced gains and reachable set bounds via dissipation inequalities. The approach is demonstrated with two examples.
The goal of this paper is to assess the robustness of an uncertain linear time-varying (LTV) system on a finite time horizon. The uncertain system is modeled as a connection of a known LTV system and a perturbation. The input/output behavior of the perturbation is described by time-domain, integral quadratic constraints (IQCs). Typical notions of robustness, e.g. nominal stability and gain/phase margins, can be insufficient for finite-horizon analysis. Instead, this paper focuses on robust induced gains and bounds on the reachable set of states. Sufficient conditions to compute robust performance bounds are formulated using dissipation inequalities and IQCs. The analysis conditions are provided in two equivalent forms as Riccati differential equations and differential linear matrix inequalities. A computational approach is provided that leverages both forms of the analysis conditions. The approach is demonstrated with two examples