Some characterizations of boundary time-varying feedbacks for fixed-time stabilization of reaction-diffusion systems. Issue 2 (2019) - Espitia, Nicolás; Polyakov, Andrey; Efimov, Denis; Perruquetti, Wilfrid
Abstract: This paper deals with continuous boundary time-varying feedbacks for fixed-time stabilization of constant-parameter reaction-diffusion systems. The time of convergence can be prescribed and is independent of the initial condition of the system. The design of time-varying feedbacks is carried out by using the backstepping approach for which suitable characterizations for time-varying kernels are derived. Kernel solutions are given in terms of power series involving the exponential complete Bell polynomials for which we have exploited the Fa à di Bruno formula . Moreover, by particularizing the characterization, one can recover kernel solutions in terms of the generalized Laguerre polynomials and the modified Bessel functions .