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Convergence Of Eigenvalues In State-Discretization Of Linear Stochastic Systems, Jose A. De Dona, Graham C. Goodwin, Richard H. Middleton, Iain Raeburn

Faculty of Engineering and Information Sciences - Papers: Part A

The transition operator that describes the time evolution of the state probability distribution for continuous-state linear systems is given by an integral operator. A state-discretization approach is proposed, which consists of a finite rank approximation of this integral operator. As a result of the state-discretization procedure, a Markov chain is obtained, in which case the transition operator is represented by a transition matrix. Spectral properties of the integral operator for the continuous-state case are presented. The relationships between the integral operator and the finite rank approximation are explored. In particular, the limiting properties of the eigenvalues of the transition matrices …