Exact controllability of singular distributed parameter control system is discussed via functional analysis and the theory of generalized operator semi-group in Hilbert space. Necessary and sufficient conditions concerning the exact controllability are given. Relations between exact controllability and stability of singular distributed parameter system are specified. exact controllability, singular distributed parameter system, Hilbert space
Perturbation and robust exponential stability of the time varying singular distributed parameter system are discussed via functional analysis and operator theory in Hilbert space. The perturbation principle of generalized evolution operators and the sufficient condition concerning the robust exponential stability of the time varying singular distributed parameter system are obtained, in which the exponential stability for the time varying singular distributed parameter system is not destroyed, if we perturb the equation by linear operator. The perturbation are assumed to have unbounded structure and the smallest perturbation which destroys exponential stability is determined.
Controllability of time varying singular distributed parameter control system is discussed via functional analysis and the theory of GE-evolution operator (i.e., generalized evolution operator) in Hilbert space. Necessary and sufficient conditions concerning the exact controllability are given.
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