Lie-Algebraic Stability Criteria for Switched Systems
SIAM Journal on Control and Optimization
Stability of Planar Switched Systems: The Linear Single Input Case
SIAM Journal on Control and Optimization
Brief paper: On the algebraic characterization of invariant sets of switched linear systems
Automatica (Journal of IFAC)
On the Stabilization of Persistently Excited Linear Systems
SIAM Journal on Control and Optimization
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This paper is concerned with asymptotic stability properties of linear switched systems. Under the hypothesis that all the subsystems share a nonstrict quadratic Lyapunov function, we provide a large class of switching signals for which a large class of switched systems are asymptotically stable. For this purpose we define what we call nonchaotic inputs, which generalize the different notions of inputs with dwell time. Next we turn our attention to the behavior for possibly chaotic inputs. Finally, we give a sufficient condition for a system composed of a pair of Hurwitz matrices to be asymptotically stable for all inputs.