Stabilization of Sampled-Data Control Systems using an Augmented Lyapunov Functional Based on Bessel-Legendre Inequality

• Grant number: 24/21859-4
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: December 01, 2025
• End date: June 01, 2026
• Field of knowledge: Engineering - Electrical Engineering - Industrial Electronics, Electronic Systems and Controls
• Principal Investigator: Rodrigo Cardim
• Grantee: Dante Javier Solis Oncoy
• Supervisor: Xianming Zhang
• Host Institution: Faculdade de Engenharia (FEIS). Universidade Estadual Paulista (UNESP). Campus de Ilha Solteira. Ilha Solteira , SP, Brazil
• Institution abroad: Swinburne University of Technology, Australia
• Associated to the scholarship: 23/05700-2 - Switched sampled-data control of Takagi-Sugeno Fuzzy systems, BP.DR

Abstract

Following doctoral studies, this research project abroad addresses the stability and stabilization of sampled-data control systems through linear matrix inequalities (LMIs) using a Lyapunov functional. First, we focus on proposing a Lyapunov functional to analyse the stability of linear systems, which is then extended to address non-linear systems modelled by a Takagi-Sugeno (T-S) fuzzy system. Secondly, we focus on proposing the design conditions of a controller to achieve stabilization for each type of system. These results will be based on the recently proposed Bessel-Legendre inequality for systems with time delay. Thus, we explore the adaptability of sampled-data control systems, addressing challenges arising from this extension, such as polynomial expressions that depends on sampling intervals. Theoretical results will be validated by numerical examples and implemented in practical systems. This document presents the formal problem statement and explains the methodology to be used. Furthermore, some limitations of existing proposals are discussed, and based on these, the specific objectives to be addressed in the project are presented. The project schedule for the period of stay abroad is also included. (AU)