On the fixed-time extinction based nonlinear control and systems decomposition: applications to bilinear systems

This paper deals with new criteria of the fixed-time extinction of nonlinear dynamical systems. We show, by comparison principal, that Gronwall-like integral inequalities leading to the extinction of the energy system in fixed-time; this helps us to build fixed-time stabilizing feedback laws for bilinear control systems in Hilbert space. In addition, in order to relax some existing results on the fixed-time stability of systems by Lyapunov function, we prove that the decomposition of the system into two subsystems so that one is finite-time stable and the other is polynomially stable, leads to fixed-time extinction of the whole system. Our results are applied to the double integrator where new fixed-time stabilizing feedbacks, with various aspects, are constructed.

Automated summary

This paper deals with new criteria for the fixed-time extinction of nonlinear dynamical systems. By comparison principal, it is shown that Gronwall-like integral inequalities can lead to the extinction of the system in fixed-time. Additionally, by decomposing the system into two subsystems, one with finite-time stability and the other with polynomial stability, the fixed-time extinction of the whole system can be achieved.