Stability control and recurrent switching rules


Correspondence to: Andrea Bacciotti, Dipartimento di Matematica del Politecnico di Torino, Duca degli Abruzzi, 24 - 10129, Torino, Italy.



Recently, 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 math formula of linear vector fields of math formula 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 math formula. We shown that, if a stabilizing eventually periodic switching rule for math formula is known, then Γ1, … ,ΓH can be constructed in such a way that math formula is stabilized by any recurrent switching rule subject to Γ1, … ,ΓH. Copyright © 2012 John Wiley & Sons, Ltd.