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• W2045786675 abstract "This paper considers the “algebraic” Riccati operator equation, which corresponds to the quadratic regulator problem for a distributed control system (it is not assumed that the operators in the cost index are positive). The assumptions used in this paper are practically important: the input space is finite-dimensional and the pair $(A,C)$ is modally observable (with respect to a suitable region $Omega $). If both these conditions hold, it is proved that the spectrum of the operator A in $dot x = Ax + Bu$ must be quite a special set, whose structure depends on the properties of the solutions to the Riccati equation. The properties of $sigma (A)$ derived in this paper must be compared with those derived in [C. A. Jacobson and C. N. Nett, IEEE Transactions on Automatic Control, AC-33 (1988), pp. 541–549] under the stabilization assumption." @default.
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• W2045786675 date "1992-07-01" @default.
• W2045786675 modified "2023-10-18" @default.
• W2045786675 title "Some Properties of Distributed Control Systems with Finite-Dimensional Input Space" @default.
• W2045786675 doi "https://doi.org/10.1137/0330051" @default.
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