# An Efficient LQR Design for Discrete-Time Linear Periodic System Based on a Novel Lifting Method

## TL;DR

This paper introduces a novel lifting method that transforms discrete-time linear periodic systems into augmented LTI systems, enabling more efficient LQR control design through specialized Riccati equation solutions.

## Contribution

A new lifting approach for periodic systems that simplifies LQR design by converting them into augmented LTI systems, improving computational efficiency.

## Key findings

- The proposed method outperforms existing algorithms in computational efficiency.
- Simulation results demonstrate successful spacecraft attitude control.
- The approach effectively simplifies periodic system control design.

## Abstract

This paper proposes a novel lifting method which converts the standard discrete-time linear periodic system to an augmented linear time-invariant system. The linear quadratic optimal control is then based on the solution of the discrete-time algebraic Riccati equation associated with the augmented linear time-invariant model. An efficient algorithm for solving the Riccati equation is derived by using the special structure of the augmented linear time-invariant system. It is shown that the proposed method is very efficient compared to the ones that use algorithms for discrete-time periodic algebraic Riccati equation. The efficiency and effectiveness of the proposed algorithm is demonstrated by the simulation test for the design problem of spacecraft attitude control using magnetic torques.