Finite Horizon Robustness Analysis of LTV Systems Using Integral Quadratic Constraints

TL;DR

This paper develops a method to analyze the robustness of uncertain linear time-varying systems over finite time horizons using integral quadratic constraints, providing computational tools for performance bounds.

Contribution

It introduces a novel finite-horizon robustness analysis framework for LTV systems using IQCs, with conditions expressed as Riccati equations and LMIs, and demonstrates its effectiveness.

Findings

Provides sufficient conditions for robustness bounds

Formulates analysis as Riccati differential equations and LMIs

Demonstrates approach with two example systems

Abstract

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