| Willems brought forward dissipation theory in 1972. It became very important conception in circuit, systems and control theory after that. Passive is a particular example of dissipation, which regards input times output as supply rate. In fact, the stabilization theory based on Lyapunov function can also be explained in view of the passivity. So the relationship between the passivity and the stability is as close as lips and teeth.Bilinear singular system is the nonlinear singular system which is the closest to linear singular system. Bilinear singular system becomes more difficult because of increasing the nonlinear item. Research of bilinear singular systems is still on the initial and developmental stage.Networked control system is the real-time closed loop feedback control system by network. There are transmission delay, data packet loss, yawp disturb in networked control systems, which make tradition control theory evaluate again before applying in networked control system. Networked control system has become one of the most popular research interests in current international control field. The research on networked control system has important theoretical meanings and also has extensive application prospects.The thesis discusses the passive of a prescribed bilinear singular system, a prescribed uncertain bilinear singular system and a prescribed networked control system. First of all, the conception of passive is introduced into these systems. Then the passive control problem is discussed under bounded energy exogenous inputs by means of linear matrix inequalities and generalized algebra Riccati inequalities, and a sufficient condition is derived as such that the prescribed singular bilinear systems and networked control systems are passive and admissible or quadratic stability. Moreover, the design method for state feedback controller is also given. At last, examples shows the feasibility of the theories. |
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