Authors: Hernan Haimovich; Alexis Vallarella; María M. Seron.
Title: Complex polytopic Lyapunov functions and componentwise ultimate bounds for switched linear systems: a missing link.
Resumen: This paper deals with switched linearsystems with persistent disturbances and under arbi-trary switching. For these systems, a systematic com-ponentwise ultimate bound computation method hasbeen previously developed. This method does not em-ploy a Lyapunov function, yet yields a mixture of ellip-soidal and polyhedral sets, which are the type of levelsets obtained via complex polytopic Lyapunov func-tions. In this context, our contribution is as follows:(a) we show that if the aforementioned component-wise method can be applied, then a complex polytopicLyapunov function exists based on which the same ul-timate bound is obtained; (b) we provide a novel al-gebraic condition for the existence of a complex poly-topic Lyapunov function of minimum complexity; (c)we give an example for which a polytopic Lyapunovfunction exists but the componentwise method cannotbe applied. These results serve to establish the preciseconnection between the two approaches.
Meeting type: Congreso.
Type of job: Artículo Completo.
Production: Complex polytopic Lyapunov functions and componentwise ultimate bounds for switched linear systems: a missing link.
Scientific meeting: XVI Reunión de Trabajo en Procesamiento de la Información y Control.
Meeting place: Córdoba.
Organizing Institution: Universidad Tecnológica Nacional / Universidad Nacional de Córdoba.
It's published?: Yes
Publication place: Córdoba
Meeting month: 10