Robust observer design for LPV systems using Kronecker sum and direct searching

This paper addresses a robust Luenberger observer for an uncertain linear parameter varying (LPV) system based on the concepts of direct searching, Kronecker sum, and small gain theorem. An algorithm is proposed to investigate the situation of the different parts of the initial observer design space, in terms of suitability for being selected as the observer gain or needing elimination due to being an undesirable part. To find the undesirable parts of the design space, the singularity of the Kronecker sum matrix of the estimation error is checked by employing the small gain theorem concept. By excluding undesired parts from the entire design space and checking the remaining parts' feasibility, a suitable solution can be found, appropriately. The performance of the proposed observer design method is illustrated by using numerical examples and an electric ground vehicle (EGV) system for the estimation of the vehicle sideslip angle and the yaw rate. The results prove the appropriateness of the designed observer using the proposed approach.