Abstract
The finite-time stabilization problem for a class of nonlinear singular systems is studied. Under the assumption that the considered system is impulse controllable, a sufficient condition is provided for the design of a state feedback control law guaranteeing the finite-time stability of the closed-loop system, and an explicit expression of the state feedback gain is also given. The proposed criterion is expressed in terms of strict matrix inequalities which is easy to be verified numerically. A numerical example is given to illustrate the effectiveness of the proposed method.
Highlights
The singular system, which is known as the semistate-space system, generalized state-space system, differential-algebraic system, implicit system, or descriptor system, is a dynamic system whose behavior is described by both differential equations and algebraic equations [1]
Compared with the concept of Lyapunov asymptotic stability, the finite-time stabilization problem studies the behavior of the dynamic system within a finite time interval
The main contribution of this paper can be given as (1) A modified and improved criterion is given for a class of nonlinear singular systems to be stabilizable, which is suitable for the case that the system matrix E is nonsingular, and suitable for the case that E is singular, and (2) The proposed criterion is formulated in terms of strict matrix inequalities without equality constraints, which has some mathematical elegance and was comparatively easy to be verified numerically
Summary
The singular system, which is known as the semistate-space system, generalized state-space system, differential-algebraic system, implicit system, or descriptor system, is a dynamic system whose behavior is described by both differential equations (or difference equations) and algebraic equations [1]. The finite-time control problems was considered for linear systems subject to time-varying parametric uncertainties and to exogenous constant disturbances [6] and a sufficient condition was given for robust finite-time stabilization via state feedback by designing a Lyapunov function with disturbance. The finite-time control problems was considered for linear systems subject to time-varying parametric uncertainties and exogenous disturbance [7], and a linear parameter-dependent state feedback gain was given by designing a Lyapunov function without disturbance, to ensure the closed-loop system to be finitetime bounded. We revisit this problem and give a sufficient condition under which the considered nonlinear singular system is finite-time stabilizable, and the explicit expression for the designed state feedback gain is given. The main contribution of this paper can be given as (1) A modified and improved criterion is given for a class of nonlinear singular systems to be stabilizable, which is suitable for the case that the system matrix E is nonsingular, and suitable for the case that E is singular, and (2) The proposed criterion is formulated in terms of strict matrix inequalities without equality constraints, which has some mathematical elegance and was comparatively easy to be verified numerically
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