Stability Analysis for A Class of Linear Hyperbolic System of Balance Laws with Sampled-data Control

Xinyong Wang (1) , Ying Tang (1) , Christophe Fiter (1) , Laurentiu Hetel (1)

1 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189

The stability for a class of linear hyperbolic systems with distributed sampled-data controllers is discussed in this paper. The original sampled-data system is firstly transformed into a new equivalent system by modelling the sampling induced error as a reset integrator operator. Then we construct an appropriate Lyapunov function and obtain sufficient conditions for the Rε-stability of the system based on linear matrix inequalities (LMIs). A numerical example illustates our results: when the sampling interval is within the allowable range, the solution of the system converges from the domain of attraction to a positive invariant set.

Mots clés: Lyapunov fuction; LMIs methods; Linear hyperbolic system; sampled-data control; Rε-stability

Domaines: Automatique / Robotique; Systèmes et contrôle [cs.SY]

Xinyong Wang, Ying Tang, Christophe Fiter, Laurentiu Hetel. Stability Analysis for A Class of Linear Hyperbolic System of Balance Laws with Sampled-data Control. IFAC World Congress, Jul 2020, Berlin, Germany. ⟨hal-02491857v2⟩