Comparative study of H2 and H-infinity cost computation methods for systems affected by polytopic uncertainties

• Grant number: 25/14208-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2025
• End date: July 31, 2026
• Field of knowledge: Engineering - Electrical Engineering
• Principal Investigator: Cecília de Freitas Morais
• Grantee: Glauco César Prado Soares
• Host Institution: Faculdade de Engenharia Elétrica e de Computação (FEEC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 24/18183-9 - Robust Control Strategies applied to networked control systems (NCS) and cyber-physical systems (CPS), AP.R

Abstract

The approaches available in the literature for computing H2 and H-infinity guaranteed costs for uncertain linear systems are mostly based on Lyapunov stability theory, generally resulting in tests formulated in terms of linear matrix inequalities (LMIs), which consist of convex optimization problems that can be solved by efficient algorithms. Particularly in the case of systems affected by uncertainties belonging to a compact set (such as polytopic systems), there are techniques in the literature that produce results with low or zero conservatism at the cost of increased computational effort, such as those that use Lyapunov functions with polynomial dependence of degree g on the parameters and cost calculation methods based on a branch-and-bound algorithm. This work aims to propose a new technique in which the guaranteed cost itself is also dependent on the uncertain parameters, in addition to conducting a comparative study with the approaches available in the literature to evaluate the trade-off between accuracy and computational effort. At the end of the research, we intend to propose an extension to treat the case of linear systems subject to Markovian jumps (Markov Jump Linear Systems - MJLS) with uncertain transition probability matrices, aiming to apply the knowledge acquired in the context of networked control systems (NCS).