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

Rabah, Rabah; Sklyar, Grigory M.; Barkhayev, Pavel Yu.

doi:10.1515/amcs-2017-0034

Cited by 13 publications

(15 citation statements)

References 32 publications

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“…Zhao and Weiss [18] establish the well-posedness, regularity, exact (approximate) controllability, and exact (approximate) observability results for the coupled systems consisting of a well-posed and regular subsystem and a finite-dimensional subsystem connected in feedback. For neutral type linear systems in Hilbert spaces, Rabah et al [19] prove that exact null controllability and complete stabilizability are equivalent. The paper also considers the case when the feedback is not bounded.…”

Section: Introductionmentioning

confidence: 99%

Controllability and Observability of Nonautonomous Riesz-Spectral Systems

Sutrima

Indrati

Aryati

2018

Abstract and Applied Analysis

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There are many industrial and biological reaction diffusion systems which involve the time-varying features where certain parameters of the system change during the process. A part of the transport-reaction phenomena is often modelled as an abstract nonautonomous equation generated by a (generalized) Riesz-spectral operator on a Hilbert space. The basic problems related to the equations are existence of solutions of the equations and how to control dynamical behaviour of the equations. In contrast to the autonomous control problems, theory of controllability and observability for the nonautonomous systems is less well established. In this paper, we consider some relevant aspects regarding the controllability and observability for the nonautonomous Riesz-spectral systems including the Sturm-Liouville systems using a 0 -quasi-semigroup approach. Three examples are provided. The first is related to sufficient conditions for the existence of solutions and the others are to confirm the approximate controllability and observability of the nonautonomous Riesz-spectral systems and Sturm-Liouville systems, respectively.

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Section: Introductionmentioning

confidence: 99%

Controllability and Observability of Nonautonomous Riesz-Spectral Systems

Sutrima

Indrati

Aryati

2018

Abstract and Applied Analysis

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“…For many purposes one need to calculate the adjoint operator A * . It was done, e.g., in Rabah [6], Rabah and Sklyar [19], but this operator has a strange form there. Therefore, we prove…”

Section: Observability For Systems Of Neutral Typementioning

confidence: 99%

“…The system (1), (3) in special case (6) with the output y(t) = Gz(t − 1) is exactly finally observable iff the two conditions hold:…”

Section: Theorem 1 (Theorem 44 In Rabah [6])mentioning

confidence: 99%

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A guaranteed state estimation of linear retarded neutral type systems

Ananyev¹

2017

AIP Conference Proceedings

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Abstract. A problem of minimax guaranteed estimation is considered for time-delayed linear systems of neutral type with uncertain input and output disturbances belonging to a ball in a Hilbert space. It is supposed that the initial state of the system is completely unknown. The infinite-dimensional informational sets are introduced in the appropriate Hilbert space and their properties are investigated. Some particular cases are considered and an example is given. The boundedness conditions for infinite-dimensional information sets which are closely connected with concept of full observability are given as well. Criteria for this are discussed. A finite-dimensional approximation scheme for the problem is discussed.

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“…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. The unbounded feedback is also investigated in the paper.…”

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

Cited by 13 publications

References 32 publications

Controllability and Observability of Nonautonomous Riesz-Spectral Systems

Controllability and Observability of Nonautonomous Riesz-Spectral Systems

A guaranteed state estimation of linear retarded neutral type systems

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

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