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Towards robust Lie-algebraic stability conditions for switched linear systems

Summary: Towards robust Lie-algebraic stability conditions for
switched linear systems
Andrei A. Agrachev, Yuliy Baryshnikov, and Daniel Liberzon
Abstract-- This paper presents new sufficient conditions for
exponential stability of switched linear systems under arbitrary
switching, which involve the commutators (Lie brackets) among
the given matrices generating the switched system. The main
novel feature of these stability criteria is that, unlike their
earlier counterparts, they are robust with respect to small per-
turbations of the system parameters. Two distinct approaches
are investigated. For discrete-time switched linear systems, we
formulate a stability condition in terms of an explicit upper
bound on the norms of the Lie brackets. For continuous-time
switched linear systems, we develop two stability criteria which
capture proximity of the associated matrix Lie algebra to a
solvable or a "solvable plus compact" Lie algebra, respectively.
A switched system is described by a family of systems and
a rule that orchestrates the switching between them (see [1]
for an overview). In the large body of literature devoted to


Source: Agrachev, Andrei - Functional Analysis Sector, Scuola Internazionale Superiore di Studi Avanzati (SISSA)


Collections: Engineering; Mathematics