Cheng-Zhong XU


  • Systèmes Non Linéaires et Procédés

Systèmes à dimension infinis

Bureau 1 LAGEP Université Claude Bernard Lyon 1, bât 308G ESCPE-Lyon, 43 bd du 11 Novembre 1918 G310 Villeurbanne 69622 France

Téléphone bureau 1: 04 72 43 18 90




Design of Integral Controllers for Nonlinear Systems Governed by Scalar Hyperbolic Partial Differential Equations

références bibliographiques:

Trinh, Ngoc-Tu, Vincent Andrieu, and Cheng-Zhong Xu. “Design of Integral Controllers for Nonlinear Systems Governed by Scalar Hyperbolic Partial Differential Equations.” , 2017, 1–1.

IEEE Transactions on Automatic Control


Multivariable boundary PI control and regulation of a fluid flow system

références bibliographiques:

Xu, Cheng-Zhong, and Gauthier Sallet. “Multivariable Boundary PI Control and Regulation of a Fluid Flow System.” 4, no. 4 (2014): 501–20.

Mathematical Control and Related Fields


New Sequence Spaces and Function Spaces on Interval

We study the sequence spaces and the spaces of functions defined on interval in this paper. By a new summation method of sequences, we find out some new sequence spaces that are interpolating into spaces between and and function spaces that are interpolating into the spaces between the polynomial space and . We prove that these spaces of sequences and functions are Banach spaces.

références bibliographiques:

Xu, Cheng-Zhong, and Gen-Qi Xu. “New Sequence Spaces and Function Spaces on Interval.” 2013 (September 24, 2013). doi:10.1155/2013/601490.

Journal of Function Spaces and Applications


Reachability-based feedback control of crystal size distribution in batch crystallization processes

In the paper, we investigate the controllability of crystallization processes by reachability analysis. Crystallization processes are governed by hyperbolic partial differential equations. Given a desired crystal size distribution, we study its reachability by the temperature control from the initial condition without seeding. When the desired crystal size distribution is reachable, we construct an admissible control steering the state to the desired distribution. Our construction is developed based on the discretized model. To ensure that the desired distribution be reached facing model uncertainty, we propose an output feedback control law to correct errors resulted from disturbed parameters of the model.

références bibliographiques:

Zhang, K., M. Nadri, and C.-Z. Xu. “Reachability-Based Feedback Control of Crystal Size Distribution in Batch Crystallization Processes.” 22, no. 10 (décembre 2012): 1856–64.

Journal of Process Control


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

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 boundary observation suffers from an arbitrary long time delay. We use the observer and predictor to solve the problem: The state is estimated in the time span where the observation is available; and the state is predicted in the time interval where the observation is not available. It is shown that the estimator/predictor based state feedback law stabilizes the delay system asymptotically or exponentially, respectively, relying on the initial data being non-smooth or smooth. Numerical simulations are presented to illustrate the effect of the stabilizing controller.

références bibliographiques:

Guo, Bao-Zhu, Cheng-Zhong Xu, and Hassan Hammouri. “Output Feedback Stabilization of a One-Dimensional Wave Equation with an Arbitrary Time Delay in Boundary Observation.” 18, no. 01 (2012): 22–35.

ESAIM: Control, Optimisation and Calculus of Variations


Eigenvalues and Eigenvectors of Semigroup Generators Obtained from Diagonal Generators by Feedback

références bibliographiques:

Xu, C.-Z., and George Weiss. “Eigenvalues and Eigenvectors of Semigroup Generators Obtained from Diagonal Generators by Feedback.” 11, no. 1 (2011): 071–104. doi:10.4310/CIS.2011.v11.n1.a5.

Communications in information and systems


Geometric synthesis of a hybrid limit cycle for the stabilizing control of a class of nonlinear switched dynamical systems

références bibliographiques:

Ben Salah, J., C. Valentin, H. Jerbi, and C.Z. Xu. “Geometric Synthesis of a Hybrid Limit Cycle for the Stabilizing Control of a Class of Nonlinear Switched Dynamical Systems.” 60, no. 12 (December 2011): 967–76. doi:10.1016/j.sysconle.2011.08.005.

Systems & Control Letters


Infinite-dimensional Luenberger-like observers for a rotating body-beam system

The paper proposes Luenberger-like observers for a rotating body-beam system. The latter is described by a partial differential equation and its dynamic is governed a unitary group. The observers proposed in the paper are able to reconstitute the dynamic evolution of the beam profile, by measuring the moment force on the boundary only. Meanwhile we propose a reliable numerical scheme, based on a finite element method, in order to simulate the observation system and the observers. The efficiency of our proposed scheme and the performances of the observers are illustrated with numerical simulation results.

références bibliographiques:

Li, Xiao-Dong, and Cheng-Zhong Xu. “Infinite-Dimensional Luenberger-like Observers for a Rotating Body-Beam System.” 60, no. 2 (2011): 138–45. doi:10.1016/j.sysconle.2010.11.005.

Systems & Control Letters


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

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 and, in particular, exponential stability of heat exchangers. Through concrete examples we show how Lyapunov’s second method may be extended to stability analysis of nonlinear hyperbolic PDE. Meanwhile we explain how the method is adapted to the framework of Banach spaces Lp , .

références bibliographiques:

Tchousso, Abdoua, Thibaut Besson, and Cheng-Zhong Xu. “Exponential Stability of Distributed Parameter Systems Governed by Symmetric Hyperbolic Partial Differential Equations Using Lyapunov’s Second Method.” 15, no. 02 (2009): 403–25. doi:10.1051/cocv:2008033.

ESAIM: Control, Optimisation and Calculus of Variations