An analysis of the input-to-state-stabilisation of linear hyperbolic systems of balance laws with boundary disturbances

2020/06/03 by Gediyon Weldegiyorgis, Weldegiyorgis, Gediyon Yemane, Mapundi K. Banda +1
Engineering · Mathematics · #49M25 #65Kxx #65L06 #Advanced Mathematical Physics Problems #FOS: Mathematics #Numerical methods for differential equations #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2006.02492

openalex publication_date 2020/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, a linear hyperbolic system of balance laws with boundary disturbances in one dimension is considered. An explicit candidate Input-to-State Stability (ISS)-Lyapunov function in L²- norm is considered and discretised to investigate conditions for ISS of the discrete system as well. Finally, experimental results on test examples including the Saint-Venant equations with boundary disturbances are presented. The numerical results demonstrate the expected theoretical decay of the Lyapunov function.

Cited by

• Feedforward boundary control of 2 × 2 nonlinear hyperbolic systems with application to Saint-Venant equations

Related

• A boundary feedback analysis for input-to-state-stabilisation of non-uniform linear hyperbolic systems of balance laws with additive disturbances
• Input-to-State Stability in sup norms for hyperbolic systems with\n boundary disturbances
• Input-to-State Stability with Respect to Boundary Disturbances for a Class of Semi-linear Parabolic Equations
• New Lyapunov functions for systems with source terms
• H₁-ISS Analysis and Boundary Control Design for Coupled Linear ODEs and Hyperbolic PDEs