Boundary feedback control of a 2×2 weakly hyperbolic system: Lyapunov-based approach (long version)
Résumé
In this paper, we propose a feedback boundary control law that ensures the exponential stability of a class of hyperbolic systems characterized by a non-diagonalizable principal part and nonuniform coefficients, as encountered in sedimentation processes and elasticity theory. We establish sufficient conditions for the exponential stability of the closedloop system. A numerical example is presented to illustrate the effectiveness of the proposed Lyapunov-based stability analysis.
Mots clés
- Linear PDE Weakly hyperbolic system with source terms Dynamic boundary conditions Nonuniform coefficients Boundary control design Stability analysis Strict Lyapunov functional
- Linear PDE
- Weakly hyperbolic system with source terms
- Dynamic boundary conditions
- Nonuniform coefficients
- Boundary control design
- Stability analysis
- Strict Lyapunov functional
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