Title :
Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems
Author_Institution :
Lab. of Adaptive & Robust Control Syst., Inst. of Control Sci., Moscow, Russia
Abstract :
Two types of nonlinear control algorithms are presented for uncertain linear plants. Controllers of the first type are stabilizing polynomial feedbacks that allow to adjust a guaranteed convergence time of system trajectories into a prespecified neighborhood of the origin independently on initial conditions. The control design procedure uses block control principles and finite-time attractivity properties of polynomial feedbacks. Controllers of the second type are modifications of the second order sliding mode control algorithms. They provide global finite-time stability of the closed-loop system and allow to adjust a guaranteed settling time independently on initial conditions. Control algorithms are presented for both single-input and multi-input systems. Theoretical results are supported by numerical simulations.
Keywords :
closed loop systems; feedback; nonlinear control systems; polynomials; stability; variable structure systems; closed-loop system; control design procedure; finite-time attractivity properties; fixed-time stabilization; global finite-time stability; linear control systems; multi-input systems; nonlinear control algorithms; nonlinear feedback design; numerical simulations; polynomial feedbacks; second order sliding mode control algorithms; single-input systems; stabilizing polynomial feedbacks; uncertain linear plants; Algorithm design and analysis; Asymptotic stability; Control systems; Convergence; Numerical stability; Polynomials; Stability analysis; Finite-time stability; polynomial feedback; second-order sliding mode control;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2011.2179869