Stability control and recurrent switching rules

• Published in: International journal of robust and nonlinear control Vol. 23; no. 6; pp. 663 - 680
• Main Author: Bacciotti, Andrea
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 01.04.2013; Wiley Subscription Services, Inc
• Subjects: asymptotic controllability; Asymptotic properties; Construction; Controllability; Mathematical analysis; Robustness; Stability; stabilization; switched systems; Switching
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.2784

SUMMARYRecently, it has been enlightened the interest of a class of switching rules with good properties, which are called eventually periodic: more precisely, it has been proven that a finite family F of linear vector fields of Rd can be stabilized by means of eventually periodic switching rules provided that it is asymptotically controllable and satisfies an additional finite time controllability condition. Unfortunately, simple examples point out that in general, eventually periodic switching rules are not robust with respect to state measurement errors.In this paper, we introduce a new type of switching rules with improved robustness properties, which are called recurrent switching rules. They are subject to the construction of a finite sequence of complete cones Γ1, … ,ΓH of Rd. We shown that, if a stabilizing eventually periodic switching rule for F is known, then Γ1, … ,ΓH can be constructed in such a way that F is stabilized by any recurrent switching rule subject to Γ1, … ,ΓH. Copyright © 2012 John Wiley & Sons, Ltd.