Finite-Time Stabilization for a Class of Nonlinear Differential-Algebraic Systems Subject to Disturbance

• Published in: Discrete dynamics in nature and society Vol. 2017; no. 2017; pp. 1 - 14
• Main Authors: Mo, Xiaohui, Lan, Qixun, Niu, Huawei
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 01.01.2017; Hindawi; John Wiley & Sons, Inc; Wiley
• Subjects: Algebra; Closed loop systems; Control systems; Controllers; Disturbances; Dynamical systems; Feedforward; Nonlinear dynamics; Nonlinear theories; Nonlinearity; Stability; Stabilization; System theory
• ISSN: 1026-0226; 1607-887X; 1607-887X
• DOI: 10.1155/2017/9730312

In this paper, finite-time stabilization problem for a class of nonlinear differential-algebraic systems (NDASs) subject to external disturbance is investigated via a composite control manner. A composite finite-time controller (CFTC) is proposed with a three-stage design procedure. Firstly, based on the adding a power integrator technique, a finite-time control (FTC) law is explicitly designed for the nominal NDAS by only using differential variables. Then, by using homogeneous system theory, a continuous finite-time disturbance observer (CFTDO) is constructed to estimate the disturbance generated by an exogenous system. Finally, a composite controller which consists of a feedforward compensation part based on CFTDO and the obtained FTC law is proposed. Rigorous analysis demonstrates that not only the proposed composite controller can stabilize the NDAS in finite time, but also the proposed control scheme exhibits nominal performance recovery property. Simulation examples are provided to illustrate the effectiveness of the proposed control approach.