Regular linear systems governed by neutral FDEs

Bounit, Hamid; Hadd, Saïd

doi:10.1016/j.jmaa.2005.07.048

Cited by 23 publications

(22 citation statements)

References 25 publications

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“…The systems are represented by absolutely regular nonautonomous linear systems in the sense of Schnaubelt [7]. These works can be considered as 2 Abstract and Applied Analysis the nonautonomous version of the works of Bounit and Hadd [8]. By employing skew-product semiflow technique, Barcenas et al [9] give necessary and sufficient conditions for exact and approximate controllability of a wide class of linear infinite-dimensional nonautonomous control systems (1).…”

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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“…Hence, Theorem 5.1 in [9] implies that the delay system (4.1) defines a well-posed system. See, e.g, [6,14] for the well-posedness of more general delay systems. Let T be the strongly continuous semigroup generating A, and define…”

Section: Application To Delay Systemsmentioning

confidence: 99%

Sampled-data output regulation of unstable well-posed infinite-dimensional systems with constant reference and disturbance signals

Wakaiki

Sano

2019

Math. Control Signals Syst.

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We study the sample-data control problem of output tracking and disturbance rejection for unstable well-posed linear infinite-dimensional systems with constant reference and disturbance signals. We obtain a sufficient condition for the existence of finite-dimensional sampled-data controllers that are solutions of this control problem. To this end, we study the problem of output tracking and disturbance rejection for infinite-dimensional discretetime systems and propose a design method of finite-dimensional controllers by using a solution of the Nevanlinna-Pick interpolation problem with both interior and boundary conditions. We apply our results to systems with state and output delays.Keywords Frequency-domain methods · Output regulation · Sampled-data control · State-space methods · Well-posed infinite-dimensional systems Mathematics Subject Classification (2010) 93B52 · 93C05 · 93C25 · 93C35 · 93C57 · 93D15

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“…In the autonomous case, i.e., when A(t) ≡ A for any t 0 and all operators in (3) are independent of time Salamon [13] has proved that the neural system (1)-(2) is well posed in the Salamon's sense (i.e., as a boundary control system with smooth initial condition and inputs). Furthermore, recently we have proved in [3] that such autonomous systems are regular in Weiss's sense [18,19]. In the current paper, we present an approach somehow similar to [3].…”

Section: Introductionmentioning

confidence: 96%

“…Furthermore, recently we have proved in [3] that such autonomous systems are regular in Weiss's sense [18,19]. In the current paper, we present an approach somehow similar to [3].…”

Section: Introductionmentioning

confidence: 96%