2024/11/18 by Vladu, Emil
#FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2411.12100
In this paper, we consider nonsymmetric solutions to certain Lyapunov and Riccati equations and inequalities with coefficient matrices corresponding to cone-preserving dynamical systems. Most results presented here appear to be novel even in the special case of positive systems. First, we provide a simple eigenvalue criterion for a Sylvester equation to admit a cone-preserving solution. For a single system preserving a self-dual cone, this reduces to stability. Further, we provide a set of conditions equivalent to testing a given H-infinity norm bound, as in the bounded real lemma. These feature the stability of a coefficient matrix similar to the Hamiltonian, a solution to two conic inequalities, and a stabilizing cone-preserving solution to a nonsymmetric Riccati equation. Finally, we show that the H-infinity norm is attained at zero frequency.