2022/03/01 by Hassan Abdelraouf, Abdelraouf, Hassan, Gidado-Yisa Immanuel +3
Engineering · #Advanced Control Systems Optimization #Control Systems and Identification #FOS: Electrical engineering #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2203.00716
openalex publication_date 2022/03/01 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
Quadratic Lyapunov function has been widely used in the analysis of linear time invariant (LTI) systems ever since it has shown that the existence of such quadratic Lyapunov function certifies the stability of the LTI system. In this work, the problem of finding upper and lower bounds for the L∞-induced norm of the LTI system is considered. Quadratic Lyapunov functions are used to find the star norm, the best upper on the L∞-induced norm, by bounding the unit peak input reachable sets by inescapable ellipsoids. Instead, a more general class of homogeneous Lyapunov functions is used to get less conservative upper bounds on the L∞-induced norm and better conservative approximations for the reachable sets than those obtained using standard quadratic Lyapunov functions. The homogeneous Lyapunov function for the LTI system is considered to be a quadratic Lyapunov function for a higher-order system obtained by Lifting the LTI system via Kronecker product. Different examples are provided to show the significant improvements on the bounds obtained by using Homogeneous Lyapunov functions.