| Controllabilities and Stabilities of switched Systems (with applications to the Quantum Systems) (2007) | |||||||||||||
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| We study various stabilities and controllabilities of linear switched systems, including those appearing in the quantum computations context. A number of new results and connections is presented, most of them with proofs. 1 Main Definitions and Problems Let us consider a set S = {Aγ: γ ∈ K}, Aγ: C n → C n. I.e., S is a set of complex n × n matrices, K is an index set. Recall that linear discrete inclusion LDI(S) is a set of discrete dynamical systems xi+1 = A R(i)xi; i ≥ 0, R: N → K. (1) Correspondingly, linear continuous inclusion LCI(S) is a set of continuous time dynamical systems X(t) ˙ = AR(t)X(t), (2) where R(.) is a piece-wise continuous from the right switching rule. LDI(S)(LCI(S)) is called Absolutely Asymptoticaly Stable (AAS) if all trajectories in (1) ((2)) converge to zero. LDI(S)(LCI(S)) is called Switching Asymptoticaly Stable (SAS) if there | |||||||||||||
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