Stability And Control Research Of Several Types Of Nonlinear Systems

In this paper, for linear time-invariant measure impulse large-scale systems and discrete nonlinear systems, the instability of linear time-invariant measure impulse large-scale systems, reduced-order observer design of one class of discrete Lipschitz nonlinear systems and suboptimal control of a class of discrete time-delay nonlinear systems are studied separately. The full text includes the following four chapters.Chapter I introduces research background and the mathematical description of the measure pulse large-scale systems and non-linear discrete systems. It gives a brief review of research progress of the measure impulse large-scale systems and non-linear discrete-time systems. It mainly includes the concept as well as the research status of impulse measure systems, the distinction with other non-consecutive ordinary differential systems, and the development together with research methods of nonlinear systems, and illustrates the limitations of these methods. Finally, it indicates some issues exit in the areas of measure pulse large-scale systems and non-linear discrete-time systems.Chapter II discusses the instability of the linear time-invariant measure impulse systems. In practical engineering, a variety of unavoidable interference always exist in a sports or work systems, and what the consequences of interference is what we have to consider. So, it is of great significance to research instability. The instability theorem of the linear time-invariant measure impulse large-scale systems is proved by Lyapunov V function and comparison principle, enriching the original theory.Chapter III studies the reduced-order observer design problem of a class of discrete Lipschitz nonlinear systems. For a class of Lipschitz nonlinear discrete systems, after the concept of the existence of observer under the meaning of Lyapunov stability is introduced and the asymptotic stability of observer errors is guaranteed, the existence of reduced-order observer is studied based on the introduced condition. The conclusion is reached that if there is a full-order observer under the meaning of Lyapunov stability with respect to the special Lyapunov function, there also exits a reduced-order one with the same assumptions. And the design of reduced-order observer is given.In chapter IV, suboptimal control is considered for a class of nonlinear discrete systems with time-delay. A suboptimal control converting method is put forward. When the control step is not more than the time-delay of the systems, suboptimal control problem can be changed into optimal control problem without time-delay by differential dynamic programming. And the design scheme of suboptimal controller is given for the systems.