Application of hybrid and polytopic modeling to the stability analysis of linear systems with saturating inputs

Abstract

This paper is concerned with the problem of stability regions determination for linear systems with saturating inputs. The paper focuses on a critical analysis of two known approaches to model the effect of actuator saturation: hybrid modeling and polytopic modeling. In each case, algorithms to determine ellipsoidal domains of stability for such class of systems are provided in terms of LMIs. The ability of such algorithms in providing large stability domains is analyzed by highlighting the main reasons they incorporate conservativeness, including the influence of the saturation modeling. Two examples are worked out illustrating how significantly the stability domains obtained by such algorithms can differ.<br>Este artigo trata do problema de determinação de regiões de estabilidade para sistemas lineares com entradas saturantes. O trabalho foca-se em uma análise crítica de duas abordagens conhecidas para o modelamento dos efeitos da saturação de controle: modelamento híbrido e modelamento politópico. Em cada caso, algoritmos para determinar domínios de estabilidade para a classe de sistemas considerada são propostos em termos de LMIs. A habilidade de tais algoritmos em fornecer grandes domínios de estabilidade é analisada, enfatizando-se as principais fontes de conservatismo, incluindo o próprio modelamento da saturação. Dois exemplos são apresentados a fim de ilustrar o quão diferente podem ser os domínios de estabilidade obtidos com os diferentes algoritmos

Robustness analysis of nonlinear systems subject to state feedback linearization

“…According to the best knowledge of the authors, there are no similar works available in the control literature that provides a methodology to estimate the domain of attraction of uncertain nonlinear systems subjected to a SFL control based on the LMI framework. Although, similar approaches dealing with saturating control laws such as (Silva Jr et al, 2004;Coutinho et al, 2004;Coutinho and Silva Jr, 2007) can be extended to cope with this problem.…”