Abstract
This paper addresses novel discrete-time and
filter designs for polytopic linear parameter-varying (LPV) systems. A less conservative approach is employed to obtain the synthesis conditions, such that the polytopic LPV system state-space representation may have all its matrices subject to time-varying parameters and be solved by an efficient procedure. Parameter-dependent Lyapunov functions are used to derive both
and
discrete-time filter design conditions resulting in a poly-quadratic approach in terms of linear matrix inequalities. A multi-objective
solution is also provided. The proposed conditions have the advantage of recovering the established poly-quadratic concept as a particular case, which was an unresolved problem until the present paper. Moreover, using the addressed approach, it is possible to obtain improved quadratic
and
filters. Numerical examples illustrate the proposed design methods applicability as an observer to estimate LPV system states and its performance in comparison with other approaches.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Data Availability Statement
Data sharing is not applicable to this article as no new data were created or analysed in this study.
Additional information
Funding
Notes on contributors
Matheus S. de Oliveira
Matheus S. de Oliveira received the B.Eng. degree in Control and Automation in 2015 and the M.S degree in Electrical Engineering in 2018 from the Pontifical Catholic University of Rio Grande do Sul - PUCRS. He is currently working toward a Ph.D. degree in Electronic Engineering at the Instituto Tecnológico de Aeronáutica - ITA. His main research interest is robust control, including uncertain systems, LPV systems, performance criteria and LMIs.
Kayol S. Mayer
Kayol S. Mayer received the B.Sc. degree in Automation and Control Engineering from the Pontifical Catholic University of Rio Grande do Sul, in 2016, and the M.Sc. degree in Electrical Engineering, also from PUCRS, in 2018. Currently, he is a Ph.D. Candidate in Electrical Engineering at the University of Campinas - Unicamp. His current research interests include wireless and optical communications, adaptive digital signal processing, and machine learning.
Renan L. Pereira
Renan L. Lima Pereira received the B.Sc. degree in electrical engineering from Federal University of Maranhão in 2009, and the M.Sc and Ph.D. degrees in electronic engineering from Instituto Tecnológico de Aeronáutica in 2011 and 2014, respectively. Since 2018, he is professor at the Instituto Tecnológico de Aeronáutica. His research interests include robust control, gain-scheduled control and optimisation.