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Boundary problems for Riccati and Lyapunov equations

Published online by Cambridge University Press:  20 January 2009

Lucas Jódar
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The resolution problem of the system

where U(t), A, B, D and Uo are bounded linear operators on H and B* denotes the adjoint operator of B, arises in control theory, [9], transport theory, [12], and filtering problems, [3]. The finite-dimensional case has been introduced in [6,7], and several authors have studied the infinite-dimensional case, [4], [13], [18]. A recent paper, [17],studies the finite dimensional boundary problem

where t ∈[0,b].In this paper we consider the more general boundary problem

where all operators which appear in (1.2) are bounded linear operators on a separable Hilbert space H. Note that we do not suppose C = −B* and the boundary condition in (1.2) is more general than the boundary condition in (1.1).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 29 , Issue 1 , February 1986 , pp. 15 - 21
Copyright
Copyright © Edinburgh Mathematical Society 1986

References

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