Abstract : Generalized monotone dilation in a Banach space is introduced. Classical theorems on existence and uniqueness of solutions of nonlinear evolution equations are revised. A universal homogeneous feedback control for a finite-time stabilization of linear evolution equation in a Hilbert space is designed using homogeneity concept. The design scheme is demonstrated for distributed finite-time control of heat and wave equations.
Andrey Polyakov, Jean-Michel Coron, Lionel Rosier. On Finite-Time Stabilization of Evolution Equations: A Homogeneous Approach. IEEE Conference on Decision and Control 2016, Dec 2016, Las Vegas, United States. ⟨hal-01371089⟩