Stabilization With Prescribed Instant for High-Order Integrator Systems

Jiyuan Kuang, Yabin Gao, Chih-Chiang Chen, Xiaoju Zhang, Yizhuo Sun, Jianxing Liu

Abstract: This article develops a new controller design approach to stabilize system states onto the equilibrium at an arbitrarily selected time instant irrespective of the initial system states and parameters. By the stabilization approach, the actual convergence time (not the bound of actual convergence time) is independent of the initial value of system states. This feature differentiates our proposed prescribed-instant stability from conventional fixed, predefined, and prescribed time stability. In this work, we propose the controller design method for the prescribed-instant stability of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${n}$ </tex-math></inline-formula> -order integrator systems. The proposed control is bounded and can gradually go to zero at an arbitrarily selected time instant, at which the system states reach zero simultaneously. This special stability of the controlled system is analyzed by reduction to absurdity. In simulations, an example of comparison with frequently used prescribed-time control is presented to show the difference. Moreover, the proposed stabilization method is validated by a magnetic suspension system with matched disturbances.