Reliable Control With Pole Constraint In A Circular Disk For Delta Operator System

With the continuous innovation and development of science and technology, Thedesign of reliable controller is very important. The failure which may be causedpossibly by the control components (actuators or sensors) should be taken intoconsideration during the process of designing the controller, which is called reliablecontrol. The purpose of it is to design a reliable controller for closed-loop system,which can maintain stable and meet certain performance indicators withoutconsidering the failure of the control components. As the model of discretization ofdelta operator tends to continuous system model when the sampling intervalT0,and then this would enable the controlled studies of continuous systems and thediscrete systems on the issue boil down to study for delta operator systems. Thefollowing problems of uncertain Delta operator systems have been studied in thispaper.First, the D-stable robust reliable control for uncertain delta operator systems ismainly studied by this article. It proposes a sufficient condition of placing poles of theclosed-loop systems in a specified circular disc, in terms of linear matrix inequalitiesby using state feedback. It also gives a design procedure of such controllers.Furthermore, a numerical example is provided to demonstrate the feasibility and theeffectiveness of the design method.Second, The pole assignment and the guaranteed cost control for uncertain deltaoperator systems are studied by this article. It provides a sufficient condition ofplacing the poles in the specified disc and the existence condition of the guaranteedcost reliable control law in terms of linear matrix inequalities by using state feedback,Lyapunov method and the pole placement method. Then, the guaranteed cost reliablecontrol with pole constrains design procedure is given by the paper. Finally, anumerical example is provided to demonstrate the feasibility and the effectiveness ofthe design method.At last, The problem of non-fragile reliable control with pole constraint in acircular disk for delta operator system is investigated in this paper. Consideringactuator fault, It proposes a sufficient condition of placing poles of the closed-loop systems in a specified circular disc by using LMI and pole placement method. Takingattenuation performance of the controller in the process of using into account, we canmake the system get greater reliability and robustness. Then, a numerical example isprovided to demonstrate the feasibility and the effectiveness of the design method.