Abstract
This paper mainly studies a control problem of finite-time boundedness of time-varying descriptor systems. Firstly, a sufficient and necessary condition of finite-time stability is given, then a sufficient condition of finite-time boundedness for time-varying descriptor systems is given. Secondly, we analyze the finite-time boundedness control problem and design the finite-time state feedback controller; the controller is given based on LMIs for time-varying descriptor systems and time-varying uncertain descriptor systems, respectively. Finally, a numerical example is given to prove the effectiveness of the method.
Highlights
IntroductionDescriptor systems (which are known as singular systems, semistate systems, systems of differential-algebraic equations, or generalized state space systems.) theory has been well studied since they are very important from the engineering point of view
Descriptor systems theory has been well studied since they are very important from the engineering point of view
We have studied the finite-time stability and given a sufficient and necessary condition of the finite-time stability; the state feedback controller was designed, we studied the finite-time boundedness of time-varying descriptor systems, and a sufficient and necessary condition of the finite-time boundedness is given and a state feedback controller was designed
Summary
Descriptor systems (which are known as singular systems, semistate systems, systems of differential-algebraic equations, or generalized state space systems.) theory has been well studied since they are very important from the engineering point of view. The time-varying descriptor system stability is mainly Lyapunov stability; Lyapunov stability deals with the whole state performance of the system, but it does not reflect a transient performance of the system. Finitetime stability of time-varying descriptor system is a new field; scholars have mainly studied the finite-time stability of linear system for years and made some corresponding results. [6–10] proposed the definition of finite-time stability and finite-time boundedness; [5–8] proposed the sufficient conditions for the finite-time stability of general linear system; [1, 11] studied the input and output finite-time stability for time-varying descriptor system. It is necessary to study finite-time stability of the time-varying uncertain descriptor system.
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