A new approach to handle additive and multiplicative uncertainties in the measurement for LPV filtering

Abstract

This paper presents a general framework to cope with full-order ${\mathcal{H}}_{\infty }$ linear parameter-varying (LPV) filter design subject to inexactly measured parameters. The main novelty is the ability of handling additive and multiplicative uncertainties in the measurements, for both continuous and discrete-time LPV systems, in a unified approach. By conveniently modelling scheduling parameters and uncertainties affecting the measurements, the ${\mathcal{H}}_{\infty }$ filter design problem can be expressed in terms of robust matrix inequalities that become linear when two scalar parameters are fixed. Therefore, the proposed conditions can be efficiently solved through linear matrix inequality relaxations based on polynomial solutions. Numerical examples are presented to illustrate the improved efficiency of the proposed approach when compared to other methods and, more important, its capability to deal with scenarios where the available strategies in the literature cannot be used.

Keywords:

• ${\mathcal{H}}_{\infty }$ filtering
• linear parameter-varying systems
• parameter-dependent filter design
• linear matrix inequalities
• inexactly measured parameters

Acknowledgements

The authors thank the anonymous reviewers for their comments and suggestions that helped to improve the paper.

Notes

1. In order to guarantee that all monomials have the same degree.

2. The symbol ⋆ means a symmetric block.

Additional information

Funding

This work was supported by two Brazilian agencies: the Federal Agency for Support and Evaluation of Graduate Education (CAPES) and the National Council for Scientific and Technological Development (CNPq), and São Paulo Research Foundation (FAPESP) [grant number 2010/10118-0].

Notes on contributors

Márcio J. Lacerda

Márcio J. Lacerda was born in Conselheiro Lafaiete, Brazil, in 1987. He received his BSc degree in electrical engineering from the Federal University of São João del-Rei, MG, Brazil, in 2009, and his MSc degree in electrical engineering from the University of Campinas, SP, Brazil, in 2010. He is currently a PhD candidate at the University of Campinas. From October 2012 to April 2013, he was a visiting student with the Laboratoire d’Analyse et d’Architecture des Systèmes, Toulouse, France. His research interests include linear systems, robust control and filtering theory.

Eduardo S. Tognetti

Eduardo S. Tognetti was born in São Paulo, Brazil, in 1979. He received his BSc and MSc degrees in electrical engineering from the University of São Paulo, in 2002 and 2006, respectively, and his PhD degree in electrical engineering from the University of Campinas – UNICAMP, in 2011. He worked as an automation engineer with the paper mill Fibria S.A. (Votorantim Pulp and Paper), from 2002 to 2011, where he was involved with industrial controllers and drive control systems. He is currently a professor at the Department of Electrical Engineering, University of Brasilia, Brasília, DF, Brazil. His research interests include stability analysis and control design of dynamical systems.

Ricardo C.L.F. Oliveira

Ricardo C.L.F. Oliveira was born in Assis Chateaubriand, Paraná, Brazil, in 1978. He received his BSc degree in computer engineering from the Pontifical Catholic University of Paraná, in 2001, and his MSc and PhD degrees in electrical engineering from the University of Campinas – UNICAMP, in 2003 and 2006, respectively. He is presently a professor at the School of Electrical and Computer Engineering, UNICAMP, SP, Brazil. His research interests include the development of numerical tools for stability analysis and control design of uncertain linear systems and fuzzy systems.

Pedro L.D. Peres

Pedro L.D. Peres was born in Sorocaba, SP, Brazil, in 1960. He received his BSc and MSc degrees in electrical engineering from the University of Campinas – UNICAMP, in 1982 and 1985, respectively, and his ‘Doctorat en Automatique’ degree from the University Paul Sabatier, Toulouse, France, in 1989. In 1990, he joined the School of Electrical and Computer Engineering, UNICAMP, SP, Brazil, where he is currently a professor. His research interests include linear systems, stability analysis, control design, convex optimisation and circuit theory.