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A geometric approach for reachability and observability of linear switched impulsive systems. (English) Zbl 1189.93021
Summary: This paper is concerned with the reachability and observability of linear switched impulsive systems with singular impulse matrices. First some new concepts with respect to the reachability and unobservability are introduced. Especially, span reachability is proposed because the reachable sets of switched impulsive systems do not always constitute subspaces. Then the geometric characterization of the span reachable and unobservable sets is presented. Moreover, the relations between the span reachable set, unobservable set and the invariant subspaces of such systems are discussed. Finally, corresponding criteria applied to linear impulsive systems and linear switched systems are also discussed.
MSC:
93B03Attainable sets
93B07Observability
93C05Linear control systems
93B27Geometric methods in systems theory
34H05ODE in connection with control problems