2019/03/18 by Bryan Van Scoy, Laurent Lessard, Van Scoy, Bryan +1
Engineering · #Advanced Control Systems Optimization #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #Vehicle Dynamics and Control Systems #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1903.07668
openalex publication_date 2019/03/18 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
We consider a linear time-invariant system in discrete time where the state\nand input signals satisfy a set of integral quadratic constraints (IQCs).\nAnalogous to the autonomous linear systems case, we define a new notion of\nspectral radius that exactly characterizes stability of this system. In\nparticular, (i) when the spectral radius is less than one, we show that the\nsystem is asymptotically stable for all trajectories that satisfy the IQCs, and\n(ii) when the spectral radius is equal to one, we construct an unstable\ntrajectory that satisfies the IQCs. Furthermore, we connect our new definition\nof the spectral radius to the existing literature on IQCs.\n