Reduced inversion methods for solving discrete periodic Riccati matrix equations

This study is concerned with the issue of solving the discrete periodic Riccati matrix equations (DPREs) in discrete-time periodic linear systems. Currently, many existing results for solving the DPRE involve matrix inversion operations. In order to diminish the matrix inversion operations, a novel reduced inversion zeroing neural network (RIZNN) model is established by constructing a set of matrix-valued error equations. Besides, a nonlinear activation function that combines a hyperbolic sine function with an exponential function is designed to accelerate the convergence rate of the RIZNN model. Specifically, with the help of a time-varying function, a prescribed-time RIZNN (PT-RIZNN) model is constructed based on the RIZNN model. The distinctive feature of the PT-RIZNN model is that the settling time can be prescribed a priori. Moreover, the convergence properties of the proposed models and the superiority of the nonlinear activation function are theoretically proven. Simulation results are supplied to demonstrate the effectiveness of the developed models and the superiority of the nonlinear activation function.