Abstract
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.
Highlights
Differential-algebraic systems (DASs) [1,2,3] known as singular systems [4,5,6,7], descriptor systems [8,9,10], or implicit systems [11] represent an important class of systems
Under the assumption that nonlinear differential-algebraic equations can be described by a nonlinear control system on a smooth manifold, the feedback stabilization problem of Nonlinear DASs (NDASs) was addressed in [15]
We will focus on solving the finite-time stabilization problem of NDASs (1a) and (1b) with the disturbance generated by the exogenous system (2)
Summary
Differential-algebraic systems (DASs) [1,2,3] known as singular systems [4,5,6,7], descriptor systems [8,9,10], or implicit systems [11] represent an important class of systems. We will consider the finite-time stabilization problem for a class of NDASs subject to external disturbance. To deal with this problem, motivated by the recently developed disturbance observer based control technique [18, 22, 23, 39, 40], a composite control approach is obtained by using the adding a power integrator technique [41] and homogeneous system theory [42]. Appendices A and B collect the preliminaries and the proofs of several key propositions, respectively
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