Stability of switched systems: a Lie-algebraic condition
نویسندگان
چکیده
منابع مشابه
Stability of switched systems: a Lie-algebraic condition∗
We present a sufficient condition for asymptotic stability of a switched linear system in terms of the Lie algebra generated by the individual matrices. Namely, if this Lie algebra is solvable, then the switched system is exponentially stable for arbitrary switching. In fact, we show that any family of linear systems satisfying this condition possesses a quadratic common Lyapunov function. We a...
متن کاملAddendum to “Stability of switched systems: a Lie-algebraic condition”
where x ∈ R, {Ap, p ∈ P} is a compact set of n × n matrices, P is an index set, and σ : [0,∞) → P is a piecewise constant switching signal. The main result of [1] (Theorem 2) states that the system (1) is globally exponentially stable, uniformly over all switching signals, if all the matrices Ap, p ∈ P are Hurwitz and the Lie algebra generated by these matrices is solvable. (Hurwitzness of the ...
متن کاملStability of switched systems : a Lie - algebraic
We present a suucient condition for asymptotic stability of a switched linear system in terms of the Lie algebra generated by the individual matrices. Namely, if this Lie algebra is solvable, then the switched system is exponentially stable for arbitrary switching. In fact, we show that any family of linear systems satisfying this condition possesses a quadratic common Lyapunov function. We als...
متن کاملLie-Algebraic Stability Criteria for Switched Systems
It was recently shown that a family of exponentially stable linear systems whose matrices generate a solvable Lie algebra possesses a quadratic common Lyapunov function, which implies that the corresponding switched linear system is exponentially stable for arbitrary switching. In this paper we prove that the same properties hold under the weaker condition that the Lie algebra generated by give...
متن کاملOn robust Lie-algebraic stability conditions for switched linear systems
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 perturbations of the system paramete...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Systems & Control Letters
سال: 1999
ISSN: 0167-6911
DOI: 10.1016/s0167-6911(99)00012-2