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2018 Controllability and Observability of Nonautonomous Riesz-Spectral Systems
Sutrima Sutrima, Christiana Rini Indrati, Lina Aryati
Abstr. Appl. Anal. 2018: 1-10 (2018). DOI: 10.1155/2018/4210135


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 C 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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Sutrima Sutrima. Christiana Rini Indrati. Lina Aryati. "Controllability and Observability of Nonautonomous Riesz-Spectral Systems." Abstr. Appl. Anal. 2018 1 - 10, 2018.


Received: 8 February 2018; Accepted: 5 April 2018; Published: 2018
First available in Project Euclid: 13 June 2018

zbMATH: 06929587
MathSciNet: MR3805988
Digital Object Identifier: 10.1155/2018/4210135

Rights: Copyright © 2018 Hindawi

Vol.2018 • 2018
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