Abstract
This paper considers the output feedback stabilization for a cascaded-wave PDE-ODE system with velocity recirculation by boundary control. First, we choose a well-known exponentially stable system as its target system and find a backstepping transformation to design a state feedback controller for the original system. Second, we attempt to give an output feedback controller for the original system by introducing the observer. The resulting closed-loop system admits a unique solution which is proved to be exponentially stable. Finally, we give some numerical examples to prove the validity for the theoretical results.
Highlights
Meglio solved the problem of stabilizing a linear ordinary differential equations (ODEs) coupled first-order hyperbolic partial differential equations (PDEs), which was based on the backstepping approach. is paper proposed a unified framework of iterative learning control for typical flexible structures under spatiotemporally varying disturbances in [20]
In [19], Meglio solved the problem of stabilizing a linear ODE coupled first-order hyperbolic PDE, which was based on the backstepping approach. is paper proposed a unified framework of iterative learning control for typical flexible structures under spatiotemporally varying disturbances in [20]
In [21], the control problem was addressed for a hybrid PDE-ODE system that described a nonuniform gantry crane system with constrained tension
Summary
The backstepping method played an important role in solving many PDEs and PDE-ODE problems, which were introduced by Krstic [27,28,29,30]. is approach was dedicated to finding an invertible Volterra integral transformation which mapped the considered plant with the boundary feedback law into a known stable target system. For some PDE-ODE systems, the authors used the backstepping approach to design the controller in [6, 7, 9,10,11,12,13,14,15,16,17,18]. Complexity backstepping method (from [30]) to achieve the stabilization of system matched disturbance with boundary control. Our main focus is on the output feedback stabilization for a cascaded-wave PDE-ODE system subject to boundary control with velocity recirculation:.
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