Open AccessState feedback ℋ ∞ control design of continuous‐time switched affine systems
Author(s) -
Deaecto Grace S.,
Santos Guilherme C.
Publication year - 2015
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2014.0153
Subject(s) - control theory (sociology) , lyapunov function , state (computer science) , affine transformation , set (abstract data type) , stability (learning theory) , exponential stability , function (biology) , mathematics , equilibrium point , upper and lower bounds , point (geometry) , control (management) , computer science , algorithm , nonlinear system , differential equation , mathematical analysis , physics , geometry , quantum mechanics , artificial intelligence , machine learning , evolutionary biology , pure mathematics , biology , programming language
This study deals with state feedback ℋ ∞ control design of continuous‐time switched affine systems. The main purpose is to design a set of state feedback gains together with a switching function assuring global asymptotic stability of a desired equilibrium point. The equilibrium point belongs to a set of attainable ones to be determined. Moreover, the control design must take into account a pre‐specified upper bound to the ℒ 2 gain from the external input to the controlled output. Two different switching functions are proposed and discussed. The first one depends only on the state and the other depends also on the external input. The results are compared with recent ones available in the literature to date, as for instance, those based on a max‐type Lyapunov function and those commonly used to assure practical stability. Numerical examples illustrate the theoretical results and are used for comparisons.