Input-to-state stabilization for a 2 × 2 hyperbolic system cascaded with an ODE
Han Wen Zhang (Shanxi University)
Jun Min Wang (Beijing Institute of Technology)
Jing Wang (TU Delft - Electrical Engineering, Mathematics and Computer Science)
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Abstract
The paper deals with the input-to-state stabilization for the 2×2 system of first-order hyperbolic equations, which convect in opposite directions cascaded with an unstable ODE equation. First, an inverse backstepping transformation is introduced to obtain a target system. Then, by active disturbance rejection control (ADRC) method, the disturbance is estimated via a disturbance estimator with time-varying gain. When the unmatched disturbances are absent, the disturbance estimator is exponentially convergent to the matched disturbance. Furthermore, in order to reject the matched disturbance and obtain the input-to-state stability of the system, the controller is proposed by using the disturbance estimator. Finally, numerical simulations are presented to validate theoretical results.