On hyper-exponential stability and stabilization of linear systems by bounded linear time-varying controllers

Abstract

Hyper-exponential stability analysis and hyper-exponential stabilization of linear systems by bounded linear time-varying feedback are investigated in this paper. On the one hand, we propose some Lyapunov-like hyper-exponential stability theorems (both global and local) based on the comparison principle and the concepts of hyper-exponentially stable functions and hyper-exponentially increasing functions. On the other hand, we establish methods to design bounded linear time-varying controllers such that hyper-exponential stability of linear time-invariant systems can be guaranteed. The key design tool is the utilization of a time-varying parameter contained in the controller and the properties of solution to a parametric Lyapunov equation. Both state feedback and observer-based output feedback are accommodated. As a further result, hyper-exponential semi-global stabilization for linear systems by bounded controls is discussed. Finally, the validity of the proposed schemes is illustrated through numerical simulations on spacecraft rendezvous control system.