IQC-based robustness analysis of discrete-time linear time-varying systems

The paper investigates the robust stability and performance of uncertain linear time-varying (LTV) systems using an integral quadratic constraint (IQC) based analysis approach. Specifically, previous theoretical work on IQC-based robustness analysis of linear time-invariant (LTI) systems is extended to discrete-time LTV systems. In the case of a general LTV nominal system, the analysis solution is provided in terms of an infinite-dimensional convex optimization problem. This optimization problem reduces into a finite-dimensional semidefinite program when the nominal system in question is finite horizon, periodic, or, more generally, eventually periodic. Finally, the results are applied to an unmanned aircraft control system executing an aggressive maneuver, where the developed techniques are used to find the region in which the aircraft is guaranteed to reside at the end of its planned trajectory.