Finite-time Control For Time-varying Descriptor Systems With Jumps

Impulse system is class of system exists in the real world which displays a certainkind of dynamics withimpulse effect at time instant, i.e., the state jumps, which cannot bedescribed by pure continuousor pure discrete models. This class of system is a more exactdescription of the influence of the sudden abrupt of the state. It is important to investigatethis kind of systems.In this thesis we investigate the finite-time control problem for time-varyingdescriptor impulsesystem. Firstly we deal with the input-output finite-time stabilityproblem for continuous-time linear time-varying descriptor system with finite jumps atfixed times. The output and input refer to the controlled output and the disturbance input,respectively. Two class of disturbance inputs are considered, which belongs to L2and L∞.We present new result for the above-mentioned class of systems in the form of sufficientconditions. The conditions are given in terms of Differential Matrix Inequalities, suchconditions requires the solution of a feasibility problem involving Differential MatrixInequalities. Based on the two conditions, state feedback controllers are designed such thatthe resultant closed-loop systems are input-output finite-time stable. With anappropriatechoice of the structure of the matrix-valued function we turn the time-varyingLMI into a ‘standard’ LMI problem and used a method to translate the non-strictLMI intostrict LMI. Finally, two examples are presented to show the validity.Next, the finite-time H∞control problem is addressed for uncertain time-varyingdescriptor system with finite jumps and time-varying norm-bounded disturbance. Firstly, asufficient condition of finite-time boundedness for the above-mentioned class of system isobtained. Then the result is extended to finite-time H∞for the system. Based on thecondition, state feedback controller is designed such that the closed-loop system isfinite-time boundedness and satisfiesL-2gain. The conditions are given in terms ofDifferential Linear Matrix Inequalities (DLMIs) and Linear Matrix Inequalities (LMIs),such conditions requires the solution of a feasibility problem involving DLMIs and LMIs,which can be solved by using existing linear algorithms. Finally, a numerical example isgiven to illustrate the effectiveness of the method.