Poles Assignment For Linear Discrete-time Periodic Systems With Time Varying Dimensions Of State And Input Spaces

In real life,the research on continuous systems is generally transformed into discrete systems.The periodic system plays an important role in linear systems,because there are many problems can be transformed into a periodic model.Therefore,study the linear discrete periodic system is very significant.Scholars have conducted in-depth research and have also achieved fruitful research results.However,there are relatively few studies on the pole assignment of linear discrete-time periodic systems with time-varying states and output dimensions,and need more research.This paper mainly studies the dimension with time-varying state and output of the pole assignment problem of linear discrete cycle system,to the problem of pole assignment through carefully reading a large number of references,the parameters of the pole assignment algorithm is proposed.This algorithm needs to transform the pole assignment problem into the problem of solving the periodic matrix equation.Therefore,this paper studies the solution of periodic matrix equation.The main contents are the following :First,the algorithm for solving the periodic matrix equations is studied and deduced.The problem of solving periodic matrix equations and the pole configuration problem of LDP systems with constant states and input dimensions are combined together,and the conditions for solution are analyzed.Under certain conditions of accuracy,an iterative solution is given.The iterative algorithm combines the splitting principle and the gradient iterative algorithm together to configure the poles of LDP systems with constant states and input dimensions.Secondly,this paper analyzes how to configure the state feedback pole for LDP systems with time-varying states and input dimensions.A two-parameter pole assignment algorithm is used to skillfully combine the pole configuration problem with the solution of the periodic matrix equation through some mathematical methods.The parameter matrix is selected randomly,and the gain matrix can be used to make the pole configuration to the pre-configured feature values.And through the algorithm to determine the closed-loop system can be configured for the conditions of the pole.Because the system will be subject to random disturbances,in order to make the system more stable,a robust state feedback pole configuration algorithm is proposed based on the parameter pole configuration algorithm.Thirdly,we discuss how to configure the output feedback pole for LDP systems with time-varying states and input dimensions.By solving the periodic matrix equations,a pole assignment algorithm for the output feedback pole of this type of system is proposed.Since the system is subject to unpredictable external disturbances in the modeling process,the controller designed for the nominal system may not be able to configure the poles of the actual system to the desired position.Therefore,it is necessary to establish a robust performance index to reflect the sensitivity of the closed-loop pole to the uncertainty,and then combine the design freedom provided by the parametric pole assignment algorithm to achieve a robust output feedback pole configuration.To sum up,the research object is a discrete periodic system with time-varying states and input dimensions.Compared with discrete periodic systems with time-invariant states and input dimensions,both the range and the depth of the system are extended,and the theoretical system is more The research on the problem of robust pole assignment for linear discrete-time periodic systems with time-varying states and input dimensions can not only lay the foundation for the robust control theory of linear discrete-time periodic systems,but also have an important meaning in control engineering practice.Therefore,it is very significant to study this problem.