Dissipative Control For A Class Of Linear Systems With Derivative Input

Dissipative theory plays an important role in the stability research of control systems since it was brought forward in1970s, the implication is that there exists a nonnegative energy function (namely storage function) such that the energy consumption of a control system is always less than the supply rate of the given supply rate. A kind of design and analytic idea is put forward in the dissipative theory, i.e. from the point of view of energy, and energy is described by input and output. Dissipative theory can contact some mathematic tools with physical phenomenon, and has been applied to many control problems. Dissipative theory has been approved to be a kind of effective method in electromechanical system, robot control and adaptive control, nonlinear H∞control and so on.We consider a class of linear systems with derivative input which is restricted equivalent transformed from singular systems and discuss its dissipativity, passivity and control problems. Firstly, compare the dissipativity of singular systems with linear systems with derivative input. After singular systems transforming into linear systems with derivative input, the dissipative conservativeness about a given supply rate reduces. Secondly, for linear systems with derivative input we design dissipative and passive state feedback controller, for time-delay linear systems with derivative input we design dissipative and passive state feedback controller and time-delay state feedback controller, such that the closed-loop systems are dissipative and passive. Eventually, numerical examples are given to demonstrate the feasibility of the theorem.