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Simulation study demonstrates exponential stabilization of parallel coupled string equations, indicating effective boundary feedback design for interconnected vibrating systems.
The article considers the boundary feedback stabilization of two parallel coupled string equations. The parallel coupled string equations are equivalently transformed into a first‐order hyperbolic equations with nonlocal terms. The control law is given by backstepping transformation. Then Lyapunov function method is used to show that the closed‐loop system is well‐posed in an space. Finally, numerical simulation results show that the state of the closed‐loop system is exponentially stable.
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Su et al. (2026) studied this question.
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