Well-Posedness and admissible stabilizability for Pritchard-Salamon systems

Guo, Faming; Zhang, Qiong; Huang, Fang‐Yang

doi:10.1016/s0893-9659(02)00145-3

Cited by 8 publications

(8 citation statements)

References 12 publications

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“…For a general theory on systems with unbounded control and observation we refer to the paper [31]. For the subclass of interest, which includes linear neutral type systems we refer to [20] and [1,5]). As our final goal is to analyze exact null controllability and complete stabilizability for neutral type systems, we will now consider a wider context of systems with unbounded input and output operators.…”

Section: Unbounded Input and Feedback Operatorsmentioning

confidence: 99%

“…Proof. In [1,Theorem 5.5] (see also [5]), in a more general situation, it is shown that system (2) with an admissible operator B is exponentially stabilizable by admissible feedback (in X 1 and X) if and only if it is exponentially stabilizable by a bounded feedback. Hence, we can suppose without loss of generality, that in (4) (2) with admissible operator B is exactly null controllable in X −1 , then it is completely stabilizable by an admissible feedback and then by a bounded feedback F.…”

Section: Unbounded Input and Feedback Operatorsmentioning

confidence: 99%

Section: Unbounded Input and Feedback Operatorsmentioning

confidence: 99%

See 2 more Smart Citations

Exact null controllability, complete stabilizability and continuous final observability of neutral type systems

Rabah

Sklyar

Barkhayev

2017

International Journal of Applied Mathematics and Computer Science

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For abstract linear systems in Hilbert spaces we revisit the problems of exact controllability and complete stabilizability (stabilizability with an arbitrary decay rate), the latter property being related to exact null controllability. We also consider the case when the feedback is not bounded. We obtain a characterization of complete stabilizability for neutral type systems. Conditions for exact null controllability of neutral type systems are discussed. By duality, we obtain a result about continuous final observability. Illustrative examples are given.

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Section: Unbounded Input and Feedback Operatorsmentioning

confidence: 99%

Section: Unbounded Input and Feedback Operatorsmentioning

confidence: 99%

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Exact null controllability, complete stabilizability and continuous final observability of neutral type systems

Rabah

Sklyar

Barkhayev

2017

International Journal of Applied Mathematics and Computer Science

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“…For the autonomous systems, Phat and Kiet [8] investigated relationship between stability and exact null controllability extending the Lyapunov equation in Banach spaces. The smart characterization of generator of the perturbation semigroup for Pritchard-Salamon systems was provided by Guo et al [9]. Rabah et al [10] prove that exact null controllability implies complete stabilizability for neutral type linear systems in Hilbert spaces.…”

Section: Introductionmentioning

confidence: 99%

Exact Null Controllability, Stabilizability, and Detectability of Linear Nonautonomous Control Systems: A Quasisemigroup Approach

Sutrima

Indrati

Aryati

2018

Abstract and Applied Analysis

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In the theory control systems, there are many various qualitative control problems that can be considered. In our previous work, we have analyzed the approximate controllability and observability of the nonautonomous Riesz-spectral systems including the nonautonomous Sturm-Liouville systems. As a continuation of the work, we are concerned with the analysis of stability, stabilizability, detectability, exact null controllability, and complete stabilizability of linear non-autonomous control systems in Banach spaces. The used analysis is a quasisemigroup approach. In this paper, the stability is identified by uniform exponential stability of the associated 0 -quasisemigroup. The results show that, in the linear nonautonomous control systems, there are equivalences among internal stability, stabizability, detectability, and input-output stability. Moreover, in the systems, exact null controllability implies complete stabilizability.is asymptotically stable in the Lyapunov sense. In this context, the system is said stabilizable and ( ) = ( ) ( ) is called the stabilizing feedback control. The complete stabilizability is one of various types of stability that is often applied to characterize the stability of the control systems. This term was

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“…Curtain et al [2] established unbounded admissible perturbation theory for PritchardSalamon systems; Guo et al [4] further improved their result to: [2,4].) Let Σ(S(·), B, C) be a Pritchard-Salamon system, F ∈ L(W, U ) be an admissible output operator and H ∈ L(Y, V ) be an admissible input operator, then …”

Section: Introductionmentioning

confidence: 99%

On the regularity and stability of Pritchard–Salamon systems

Huang

2006

Journal of Mathematical Analysis and Applications

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Let Σ(S(·), B, −) be a Pritchard-Salamon system for (W, V ), where W and V are Hilbert spaces. Suppose U is a Hilbert space and F ∈ L(W, U ) is an admissible output operator, S BF (·) is the corresponding admissible perturbation C 0 -semigroup. We show that the C 0 -semigroup S BF (·) persists norm continuity, compactness and analyticity of C 0 -semigroup S(·) on W and V , respectively. We also characterize the compactness and norm continuity of ∆ BF (t) = S BF (t) − S(t) for t > 0. In particular, we unexpectedly find that ∆ BF (t) is norm continuous for t > 0 on W and V if the embedding from W into V is compact. Moreover, from this we give some relations between the spectral bounds and growth bounds of S BF (·) and S(·), so we obtain some new stability results.

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Well-Posedness and admissible stabilizability for Pritchard-Salamon systems

Cited by 8 publications

References 12 publications

Exact null controllability, complete stabilizability and continuous final observability of neutral type systems

Exact null controllability, complete stabilizability and continuous final observability of neutral type systems

Exact Null Controllability, Stabilizability, and Detectability of Linear Nonautonomous Control Systems: A Quasisemigroup Approach

On the regularity and stability of Pritchard–Salamon systems

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