Multivariable boundary PI control and regulation of a fluid flow system

Cheng-Zhong Xu (1) , Gauthier Sallet (2, 3)

1 LAGEP - Laboratoire d'automatique et de génie des procédés
2 MASAIE - Tools and models of nonlinear control theory for epidemiology and immunology
3 IECL - Institut Élie Cartan de Lorraine

The paper is concerned with the control of a fluid flow system gov-erned by nonlinear hyperbolic partial differential equations. The control and the output observation are located on the boundary. We study local stability of spatially heterogeneous equilibrium states by using Lyapunov approach. We prove that the linearized system is exponentially stable around each subcritical equilibrium state. A systematic design of proportional and integral controllers is proposed for the system based on the linearized model. Robust stabilization of the closed-loop system is proved by using a spectrum method.

Mots clés: spatially heterogeneous equilibrium states; Hyperbolic partial differential equations; exponential stability; spectrum assignment; robust stabilization

Domaines: Systèmes dynamiques [math.DS]; Mathématiques générales [math.GM]

Cheng-Zhong Xu, Gauthier Sallet. Multivariable boundary PI control and regulation of a fluid flow system. Mathematical Control and Related Fields, 2014, 4 (4), pp.501 - 520. ⟨10.3934/mcrf.2014.4.501⟩. ⟨hal-01086097⟩