Regular linear systems with feedback

Abstract-A new functional analytic approach to the concept of feedback stabilizability of infinite dimensional linear neutral systems is presented. We first reformulate this systems as an infinite dimensional open-loop systems with appropriate semigroups and unbounded control operators. We introduce conditions for which such semigroups are eventually compact. In addition, when the image of the control operator is finite dimensional, we give necessary and sufficient conditions for the feedback stabilizability of neutral system. Our approach is based on the concept of regular linear systems in the Salamon-Weiss sens.

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“…The following theorem is due to Weiss in Hilbert spaces [39] and to Staffans in general Banach spaces [33,Chap.7].…”

Section: Definition 23mentioning

confidence: 99%

“…For the reader's convenience, in Section II we briefly recall the relevant background of regular linear system from [32], [33], [39]. In Section III we present the reformulation of the neutral system (1) as a distributed linear system.…”

Section: Introductionmentioning

confidence: 99%

Feedback stabilizability of infinite dimensional neutral systems

Hadd

Nounou

2010

49th IEEE Conference on Decision and Control (CDC)

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“…Part (i) follows easily from the equivalence of (1) and (4) Let us remark that our operator C is a restriction of the operator that Weiss denotes by C L in [45] and by C Λ in [46], and also a restriction of Weiss' operator C L . He does not explicitly study B * and the time-invariant setting.…”

Section: The Generators Of a Well-posed Linear Systemmentioning

confidence: 99%

“…This theory has been developed in [33], [34], [35], [8], [11], and [43], [44], [45], [46] (and many other papers), and we refer the reader to these sources for additional reading. (Salamon calls these systems "well-posed semigroup control systems" and Weiss calls them "abstract linear systems".)…”

Section: Well-posed Linear Systems and Time-invariant Operatorsmentioning

confidence: 99%

“…As Weiss [46,Section 6] proved, x and y in (23) To get a better feeling for the feedback formula in Proposition 20 we recommend that the reader carry out the following exercise. If in the classical system (1) we replace u by u = Ly + v, then we get a new well-defined system of the same type iff I − DL is invertible, or equivalently, iff I − LD is invertible.…”

Section: Static Output Feedback State Feedback and Output Injectionmentioning

confidence: 99%

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Quadratic optimal control of stable well-posed linear systems

Staffans

1997

Trans. Amer. Math. Soc.

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Abstract. We consider the infinite horizon quadratic cost minimization problem for a stable time-invariant well-posed linear system in the sense of Salamon and Weiss, and show that it can be reduced to a spectral factorization problem in the control space. More precisely, we show that the optimal solution of the quadratic cost minimization problem is of static state feedback type if and only if a certain spectral factorization problem has a solution. If both the system and the spectral factor are regular, then the feedback operator can be expressed in terms of the Riccati operator, and the Riccati operator is a positive self-adjoint solution of an algebraic Riccati equation. This Riccati equation is similar to the usual algebraic Riccati equation, but one of its coefficients varies depending on the subspace in which the equation is posed. Similar results are true for unstable systems, as we have proved elsewhere.

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On the distributed stable full information H minimax problem

Staffans

1998

Int. J. Robust Nonlinear Control

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Regular linear systems with feedback

Cited by 266 publications

References 10 publications

Feedback stabilizability of infinite dimensional neutral systems

Feedback stabilizability of infinite dimensional neutral systems

Quadratic optimal control of stable well-posed linear systems

On the distributed stable full information H minimax problem

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