On componentwise ultimate bound minimisation for switched linear systems via closed-loop Lie-algebraic solvability
نویسندگان
چکیده
منابع مشابه
On componentwise ultimate bound minimisation for switched linear systems via closed-loop Lie-algebraic solvability
We present a novel state feedback design method for perturbed discrete-time switched linear systems. The method aims at achieving (a) closed-loop stability under arbitrary switching and (b) minimisation of ultimate bounds for specific state components. Objective (a) is achieved by computing state feedback matrices so that the closed-loop A matrices generate a solvable Lie algebra (i.e. admit si...
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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...
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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...
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ژورنال
عنوان ژورنال: IFAC Proceedings Volumes
سال: 2014
ISSN: 1474-6670
DOI: 10.3182/20140824-6-za-1003.02663