Abstract
In §2.1 and §2.2 of Chapter 1 of Part I, we have discussed criteria for controllability, and observability for finite dimensional systems and have also shown that when the system is controllable we can transfer the state z0 ∈ H at time t0 to the state z1 ∈ H at time t1 using minimum energy controls. These results were obtained by considering the controllability operator
and its adjoint
and studying the relation between the ranges and null spaces of these two operators and by showing that controllability is equivalent to invertibility of LTL * T . As we have remarked (see Remark 2.1, Chapter 1 of Part I) in some sense the same ideas can be used to obtain characterizations of controllability when the spaces U and X are infinite dimensional Hilbert spaces, but at the expense of using much elaborate technical machinery. In this chapter we discuss questions of controllability for parabolic and second-order hyperbolic equations, the plate equation, and Maxwell’s equations.
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© 2007 Birkhäuser Boston
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(2007). Controllability and Observability for a Class of Infinite Dimensional Systems. In: Representation and Control of Infinite Dimensional Systems. Systems & Control: Foundations & Applications. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4581-6_8
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DOI: https://doi.org/10.1007/978-0-8176-4581-6_8
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4461-1
Online ISBN: 978-0-8176-4581-6
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