Stability and control of nonlinear Lur'e systems by means of linear matrix inequalities

Author(s)

Ariádne de Lourdes Justi Bertolin

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Elétrica e de Computação
• Defense date: 2023-07-18

Examining board members

Pedro Luis Dias Peres; Paulo Augusto Valente Ferreira; Eugênio de Bona Castelan Neto; João Manoel Gomes da Silva Jr.; Juan Francisco Camino

• Advisor: Pedro Luis Dias Peres

Abstract

This thesis investigates the problem of stability analysis and control design for Lur’e nonlinear systems in discrete- and continuous-time. The Lur’e systems are characterized by a linear time-invariant (LTI) plant with the feedback of sector or slope bounded nonlinearities. Absolute stability certification for Lur’e systems is obtained only from the information of the LTI system, and the sector or slope bounds. In this thesis, two approaches are used to compute stability certificates: the Lyapunov method and Zames-Falb (ZF) multipliers. In both cases, the proposed analysis and synthesis conditions are formulated in terms of iterative algorithms based on linear matrix inequalities (LMIs). The main technical novelty is the possibility of designing output feedback controllers (dynamic and static) employing, for example, approaches based on integral quadratic constraints (IQCs). Furthermore, in the context of ZF multipliers, the proposed method is innovative because it enables the synthesis of output feedback controllers adopting multipliers of arbitrary order. As an extension of the ZF multipliers method, conditions for analysis and control design for linear systems using the L1 norm as performance criterion are also provided. Numerical experiments illustrate the proposed methods in system models borrowed from the literature and on sets of randomly generated systems, allowing for a comparative analysis of the proposed conditions (AU)

• FAPESP's process: 19/10947-1 - Stability, control and filtering for uncertain dynamical systems by means of linear matrix inequalities
• Grantee: Ariádne de Lourdes Justi Bertolin
• Support Opportunities: Scholarships in Brazil - Doctorate