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Exponential stability and transfer functions of processes governed by symmetric hyperbolic systems

Cheng-Zhong XuGauthier Sallet — 2002

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study the frequency and time domain behaviour of a heat exchanger network system. The system is governed by hyperbolic partial differential equations. Both the control operator and the observation operator are unbounded but admissible. Using the theory of symmetric hyperbolic systems, we prove exponential stability of the underlying semigroup for the heat exchanger network. Applying the recent theory of well-posed infinite-dimensional linear systems, we prove that the system is...

Exponential Stability and Transfer Functions of Processes Governed by Symmetric Hyperbolic Systems

Cheng-Zhong XuGauthier Sallet — 2010

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study the frequency and time domain behaviour of a heat exchanger network system. The system is governed by hyperbolic partial differential equations. Both the control operator and the observation operator are unbounded but admissible. Using the theory of symmetric hyperbolic systems, we prove exponential stability of the underlying semigroup for the heat exchanger network. Applying the recent theory of well-posed infinite-dimensional linear systems, we prove that the system...

Output feedback stabilization of a one-dimensional wave equation with an arbitrary time delay in boundary observation

Bao-Zhu GuoCheng-Zhong XuHassan Hammouri — 2012

ESAIM: Control, Optimisation and Calculus of Variations

The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stability of closed-loop system achieved by some stabilizing output feedback laws may be destroyed by whatever small time delay there exists in observation. In this paper, we are concerned with a particularly interesting case: Boundary output feedback stabilization of a one-dimensional wave equation system for which the...

Output feedback stabilization of a one-dimensional wave equation with an arbitrary time delay in boundary observation

Bao-Zhu GuoCheng-Zhong XuHassan Hammouri — 2012

ESAIM: Control, Optimisation and Calculus of Variations

The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stability of closed-loop system achieved by some stabilizing output feedback laws may be destroyed by whatever small time delay there exists in observation. In this paper, we are concerned with a particularly interesting case: Boundary output feedback stabilization of a...

Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using Lyapunov’s second method

Abdoua TchoussoThibaut BessonCheng-Zhong Xu — 2009

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study asymptotic behaviour of distributed parameter systems governed by partial differential equations (abbreviated to PDE). We first review some recently developed results on the stability analysis of PDE systems by Lyapunov’s second method. On constructing Lyapunov functionals we prove next an asymptotic exponential stability result for a class of symmetric hyperbolic PDE systems. Then we apply the result to establish exponential stability of various chemical engineering processes...

Output feedback stabilization of a one-dimensional wave equation with an arbitrary time delay in boundary observation

Bao-Zhu GuoCheng-Zhong XuHassan Hammouri — 2012

ESAIM: Control, Optimisation and Calculus of Variations

The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stability of closed-loop system achieved by some stabilizing output feedback laws may be destroyed by whatever small time delay there exists in observation. In this paper, we are concerned with a particularly interesting case: Boundary output feedback stabilization of a...

Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using Lyapunov's second method

Abdoua TchoussoThibaut BessonCheng-Zhong Xu — 2008

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study asymptotic behaviour of distributed parameter systems governed by partial differential equations (abbreviated to PDE). We first review some recently developed results on the stability analysis of PDE systems by Lyapunov's second method. On constructing Lyapunov functionals we prove next an asymptotic exponential stability result for a class of symmetric hyperbolic PDE systems. Then we apply the result to establish exponential stability of various chemical engineering processes...

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