Stability and Stabilization of Infinite Dimensional Systems with Applications

Luo, Zheng-Hua; Guo, Bao‐Zhu; Morgül, Ömer; Sontag, Eduardo D.; Modestino, J.W.; Thoma, M.; Dickinson, B. W.; Fettweis, A.; Massey, James L.

doi:10.1007/978-1-4471-0419-3

Cited by 429 publications

(340 citation statements)

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“…With this work we showed that appropriate physical modeling is of great interest to prove properties of solutions associated to boundary control systems. Finally, we can remark that the class of systems treated in this paper is large enough to deal with well known examples from the literature as coupled wave equation (see [16], Chap. 6, and [3]), Timoshenko beam equation, convection equation.…”

Section: Resultsmentioning

confidence: 99%

Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain

et al. 2009

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Abstract.We study a class of hyperbolic partial differential equations on a one dimensional spatial domain with control and observation at the boundary. Using the idea of feedback we show these systems are well-posed in the sense of Weiss and Salamon if and only if the state operator generates a C0-semigroup. Furthermore, we show that the corresponding transfer function is regular, i.e., has a limit for s going to infinity.Mathematics Subject Classification. 93C20, 35L40, 35F15, 37Kxx.

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Section: Resultsmentioning

confidence: 99%

Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain

et al. 2009

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“…Now let us introduce the notion of strict Lyapunov function that is considered in this paper (see Luo et al [1999] for the definition of a Lyapunov function).…”

Section: Singularly Perturbed System Of Conservation Lawsmentioning

confidence: 99%

Lyapunov stability of a singularly perturbed system of two conservation laws

Tang

Prieur²,

Girard³

2013

IFAC Proceedings Volumes

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This paper is concerned with a class of singularly perturbed systems of two conservation laws. A small perturbation parameter is introduced in the dynamics and the boundary conditions. By setting the perturbation parameter to zero, the singularly perturbed system of conservation laws can be treated as two subsystems of one conservation law: the reduced system and the boundary-layer system. The asymptotic stability of the complete system is investigated via Lyapunov techniques. A Lyapunov function for the singularly perturbed system is obtained as a weighted sum of two Lyapunov functions of the subsystems.

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“…The analysis of the following results is based on concepts and results developed e.g. in [9,14,19,21].…”

Section: Stability Analysismentioning

confidence: 99%

Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems

2008

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Abstract. The Linear-Quadratic (LQ) optimal control problem is studied for a class of first-order hyperbolic partial differential equation models by using a nonlinear infinite-dimensional (distributed parameter) Hilbert state-space description. First the dynamical properties of the linearized model around some equilibrium profile are studied. Next the LQ-feedback operator is computed by using the corresponding operator Riccati algebraic equation whose solution is obtained via a related matrix Riccati differential equation in the space variable. Then the latter is applied to the nonlinear model, and the resulting closed-loop system dynamical performances are analyzed. Mathematics Subject Classification.

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Stability and Stabilization of Infinite Dimensional Systems with Applications

Cited by 429 publications

References 0 publications

Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain

Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain

Lyapunov stability of a singularly perturbed system of two conservation laws

Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems

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