A characterization of switched linear control systems with finite L 2 -gain

Motivated by an open problem posed by J.P. Hespanha, we extend the notion of Barabanov norm and extremal trajectory to classes of switching signals that are not closed under concatenation. We use these tools to prove that the finiteness of the L2-gain is equivalent, for a large set of switched linear control systems, to the condition that the generalized spectral radius associated with any minimal realization of the original switched system is smaller than one

Invariance principles for switched systems with restrictions

In this paper we consider switched nonlinear systems under average dwell time switching signals, with an otherwise arbitrary compact index set and with additional constraints in the switchings. We present invariance principles for these systems and derive by using observability-like notions some convergence and asymptotic stability criteria. These results enable us to analyze the stability of solutions of switched systems with both state-dependent constrained switching and switching whose logic has memory, i.e., the active subsystem only can switch to a prescribed subset of subsystems.Comment: 29 pages, 2 Appendixe

Singular Switched Systems in Discrete Time: Solvability, Observability, and Reachability Notions

Discrete-time singular (switched) systems, also known as(switched) difference-algebraic equations and discrete-time (switched)descriptor systems, have in general three solvability issues:inconsistent initial values, nonexistence ornonuniqueness of solutions, and noncausalities, which are generallynot desired in applications. To deal with those issues, newsolvability notions are proposed in the study, and the correspondingnecessary and sufficient conditions have been derived with the help of(strictly) index-1 notions. Furthermore, surrogate (switched)systems--ordinary (switched) systems that have equivalentbehavior--have also been established for solvable systems. Byutilizing those surrogate systems, fundamental analysis includingobservability, determinability, reachability, and controllability has also beencharacterized for singular linear (switched) systems. The solvabilitystudy has been extended to singular nonlinear (switched) systems, andmoreover, Lyapunov and incremental stability analyses have beenderived via single and switched Lyapunov function approaches