We are delighted to extend our congratulations to Dr. Shivarj Mohite on the successful completion of his PhD journey, with thesis title "Observer Design for Nonlinear Systems using LMI Relaxation Techniques". He defended his thesis on 20th December, 2023 in IAEM doctoral school, University of Lorraine, France.

Over the past three decades, the design of observers for dynamic systems has become an important topic in the field of control systems. This thesis focuses on observer design using LMIs relaxation techniques for classes of Lipschitz nonlinear systems. The main contribution of the thesis is the proposal of new matrices called “Matrix-Multiplier”. The LMIs conditions obtained using these matrices (as well as a reformulation of the Lipschitz property and the Young relation in a judicious way) are less restrictive than other existing techniques in the literature. An extension to the H_∞ case has been proposed for the disturbance-affected nonlinear systems. Further, the proposed matrix multiplier-based LMI approach is exploited for the stabilization of nonlinear systems affected by disturbances using observer-based control. The judicious implementation of LMIs based on matrix multipliers resulted in less conservative LMI conditions than existing LMI methods in the literature. Finally, all these developed LMI-based observers are used in the field of autonomous vehicles for various tasks, such as longitudinal state estimation, slip angle estimation, etc., to validate their performance.

We wish Dr. Mohite all the best in his future endeavors, and we look forward to see the impact of his research in the field. Congratulations once again on this extraordinary achievement.