Finite-time Control Of Time-varying Descriptor Impulse Systems

Impulse system is class of system exists in the production and living of human society and science of technology, the jumps, which cannot be described by pure differential or differential equations to describe, but with suitable impulse differential equations to describe. The benefits of the use of impulse differential equations to describe the kind of problem that Impulsive Differential Equations to take into account the state of the system in an instant burst effect on the whole system and could description of the influence of the impulse phenomenon. It is very significance and value to investigate this kind of systems.In this thesis it investigates the finite-time control problem for time-varying descriptor impulse system. Firstly, it deals with the finite-time stability problem for linear time-varying descriptor impulse systems. Consider the generalized system proved itself in the context of non-impulsive effect, the necessary and sufficient conditions for linear time-varying descriptor impulsive systems to be finite-time stable are proposed in terms of a set of Differential Matrix Inequalities. Then, the problem of robust finite-time stability for linear time-varying descriptor impulsive systems is addressed. And the sufficient conditions for the systems to be robust finite-time stable is proposed. Finally, a numerical example is given to verify the validity of the obtained theoretical results of this chapter.Next, the State-dependent finite-time stability problem is addressed for continuous-time linear time-varying descriptor impulse systems. The sufficient conditions for State-dependent continuous-time linear time-varying descriptor impulse systems to be finite-time stable are proposed in terms of a set of Differential Matrix Inequalities and the S-procedure arguments. It makes such problems easier to handle on a numerical calculation. Based on the conditions above, state feedback control law is designed such that the closed-loop systems is finite-time stable. Finally, a numerical simulation is presented to verify the validity of the obtained theoretical results of this chapter.