A new approach for stabilization of Heat-ODE cascaded systems with boundary delayed control

Zhang, Li; Xu, Guan; Mastorakis, Nikos E.

doi:10.1093/imamci/dnab037

Cited by 2 publications

(1 citation statement)

References 41 publications

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“…Based on engineering applications of subsea installation of deep-water construction vessels for oil drilling, Wang and Krstic (2020) studied output feedback boundary control problem for PDEs (hyperbolic) sandwiched between two ODEs. We refer interested readers to the studies Weiss and Zhao, (2011) and Zhang et al, (2022) for other results.…”

Section: Introductionmentioning

confidence: 99%

State feedback controller design of fractional ordinary differential equations coupled with a fractional reaction–advection–diffusion equation with delay

Hou

Zhou

2023

Transactions of the Institute of Measurement and Control

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The boundary control problem of fractional ordinary differential equations coupled with a time fractional reaction–advection–diffusion equation with delay is studied in this paper. To ensure the asymptotic stability of the system we studied, a state feedback boundary controller is proposed. By backstepping method, we transform the fractional coupled system into a chosen target system under a controller. Furthermore, we obtain the existence and uniqueness of the state solution of the considered system. A Lyapunov functional is constructed to show the asymptotic stability of the fractional coupled system by the special fractional Halanay inequality. The asymptotic stability criterion of the fractional coupled system is described by Linear Matrix Inequalities (LIMs). Which can be easily solved and verified. Finally, the applicability of our theoretical results is showed by a numerical simulation.

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Section: Introductionmentioning

confidence: 99%

State feedback controller design of fractional ordinary differential equations coupled with a fractional reaction–advection–diffusion equation with delay

Hou

Zhou

2023

Transactions of the Institute of Measurement and Control

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Uniform stabilization of a Schrödinger equation with partial Dirichlet delayed control

Wang,

2023

IMA Journal of Mathematical Control and Information

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In this paper, the uniform stabilization of a multi-dimensional Schrödinger equation with partial Dirichlet delayed control is concerned. The control input is suffered from time delay. Herein a new feedback controller is adopted in the investigation. Firstly, we rewrite the delayed system under consideration into a cascaded system of a transport equation and a Schrödinger equation, and construct an exponentially stable target system. Then by defining a bounded invertible linear transformation and choosing some appropriate kernel functions, we establish the equivalence between the closed-loop system and the target system. Finally, the exponential stability of the closed-loop system is obtained.

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A new approach for stabilization of Heat-ODE cascaded systems with boundary delayed control

Cited by 2 publications

References 41 publications

State feedback controller design of fractional ordinary differential equations coupled with a fractional reaction–advection–diffusion equation with delay

State feedback controller design of fractional ordinary differential equations coupled with a fractional reaction–advection–diffusion equation with delay

Uniform stabilization of a Schrödinger equation with partial Dirichlet delayed control

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