Linear Singular System Is Strictly Dissipative Control Based On Observer

Singular system is a kind of dynamics of more general and has a wide application background. It is a powerful tool which can describe and depict control system and has a very profound practical applications. Singular system has been developed sufficiently from 1970s, and many classical concepts and results in the normal state space theory have been extended to singular systems.Dissipative theory generalizes the bounded real lemma,circle criterion theorem, H∞theory, Kalman-Yacubovitch lemma. The study of general dissipative control problem is that it offers a unified framework for solving the problems of H∞control and positive real control. Further, it can reveal a lot of more profound content.In real system, the state variable is usually not measured directly and other conditions or restrictions can not be achieved, so it need use the input and output to construct the state observer, making the output approaching observer state vector. Observer-based control design is a necessary means and effective way.The paper mainly deal with the problem of designing state observer-based strictly dissipative controller,general form observer-based strictly dissipative controller,reduced order observer-based strictly dissipative controller for linear singular systems respectively. By using the Lyapunov function and linear matrix inequality (LMI) method, sufficient conditions are obtained for the existences of the observers and the controllers, and the corresponding design methods are also given in terms of the solutions of linear matrix inequalities (LMI). The above conditions can guarantee that the observers track the system state asymptotically and the closed-loop singular systems are admissible (i.e. regular, stable and impulse free) and strictly dissipative. Finally, several numerical examples and the simulation results are provided to demonstrate the validity and effectiveness of the proposed method.