Integral input-to-state stabilization of a class of parabolic systems with time-varying coefficients
For parabolic systems with time-varying coefficients,it remains a challenging problem how to design a boundary feedback control via a time-invariant kernel function for ensuring the stability of the closed-loop system.In this paper,the problem of stabilization of certain class of parabolic systems with space-time-varying coefficients is investigated.Specifically,without applying a Gevrey condition and an event-triggered scheme,a boundary feedback controller is de-signed by using a time invariant kernel function.Meanwhile,in order to characterize the influence of external disturbances on the stability of the system,the stability of the closed-loop system is studied in the framework of input-to-state stability theory(ISS theory).In particular,the L1-ISS of the considered system is established in the spatial L1-norm by using the approximative Lyapunov method and comparison principle for parabolic PDEs with nonlocal boundary conditions.The validity of the controller and the proposed approach are further verified by numerical simulations.
integral input-to-state stabilitybacksteppingstabilizationapproximative Lyapunov methodcomparison principleparabolic equationtime-varying coefficient
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