Filter design for linear systems with H-2, H-infinity and H-infinity in frequency interval criteria by means of matrix inequalities

Author(s)

Lício Bruno Ribeiro Rodrigues Romão

• Document type: Master's Dissertation
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Elétrica e de Computação
• Defense date: 2017-02-09

Examining board members

Pedro Luis Dias Peres; Juan Francisco Camino; Matheus Souza

• Advisor: Pedro Luis Dias Peres

Abstract

This thesis is devoted to the problem of filter design for linear dynamic systems using the Linear Matrix Inequality (LMI) framework. More precisely, LMI based conditions for the design of full-order filters for continuous- and discrete-time linear systems, using the H-2 and H-infinity norms as performance criteria, are proposed, with extensions to deal with polytopic uncertainty. The conditions have a scalar parameter and become LMIs for fixed values of the scalar. As attractive characteristics, the proposed conditions dissociate the Lyapunov matrix, that certifies the stability and the H-infinity or H-2 performance, from the matrices of the filter realization, encompassing the well-known quadratic stability based results from the literature for specific values of the scalar parameter. Additionally, the H-infinity filtering problem with low, middle and high frequency specifications is addressed through an extension of the Kalman-Yakubovich-Popov Lemma that relates frequency domain inequalities on line or circle segments with matrix inequalities. LMI based conditions for the design of H-infinity filters satisfying frequency range specifications with a stable realization and real matrices are proposed, for both continuous- and discrete-time cases, as well as extensions to cope with uncertain systems. Numerical examples illustrate the proposed results (AU)

• FAPESP's process: 14/06408-4 - Matrix Inequalities with Scalars for Robust Filtering Design
• Grantee: Lício Bruno Ribeiro Rodrigues Romão
• Support Opportunities: Scholarships in Brazil - Master