Sampling Observer Design And Control Synthesis For MIMO Nonlinear Differential-Algebraic Equations System

In this paper,the design of sampled-output state observer and further sampled-output feedback stabilization controller for a class of multi-input multi-output nonlinear differential-algebraic systems with index 1 is studied.The main contents are as follows:1.The concept of uniform relative order for MIMO nonlinear ordinary differential systems is extended,and the necessary and sufficient conditions for equivalent transformation of the systems are given.2.Sampling observer design for multi-input multi-output nonlinear differential-algebraic systems is studied.·Under the Lipschitz condition,an initial sampled-output state observer is constructed based on the equivalent system.At this time,the initial state of the system needs to satisfy the algebraic constraint equation.Finally,it is proved that there exists an appropriate sampling period,which makes the proportional observation error converge to zero.·Still based on the equivalent system,a class of non-initialized sampled-output state observers is constructed.At this time,the initial state of the system is not limited to algebraic constraints.Combining with Lyapunov stability theory,the appropriate sampling period and gain parameters are derived to ensure that the proportional observation error converges to zero.3.The design of sampled-output feedback stabilization control for MIMO nonlinear differential-algebraic systems is studied.·Under the condition of satisfying linear growth,a class of state observers for linear explicit initial sampled output are given based on equivalent systems,which does not require precise knowledge of the non-linear terms,and have better robust stability.A linear sampled controller is constructed by using observers.With the help of Lyapunov stability theory,sufficient conditions for the stability of the whole closed-loop system are given,and appropriate sampling cycles are selected.The period and gain parameters make the closed-loop system asymptotically stable.·Based on the equivalent system,a class of non-initialized sampled-output state observers with linear display are given.The linear sampled-output state observers are constructed according to the estimated values of the system observations.Combining with Lyapunov stability theory,the formula of the appropriate sampling period and the range of the gain parameters are obtained,so that the closed-loop system is asymptotically stable.