On the State-Feedback Controller Design for Polynomial Linear Parameter-Varying Systems with Pole Placement within Linear Matrix Inequality Regions

Jorge A. Brizuela-Mendoza, Juan Carlos Mixteco-Sánchez, Maria A. López-Osorio, Gerardo Ortiz-Torres (), Felipe D. J. Sorcia-Vázquez, Ricardo Eliú Lozoya-Ponce, Moises B. Ramos-Martínez, Alan F. Pérez-Vidal, Jesse Y. Rumbo Morales, Cesar H. Guzmán-Valdivia, Mayra G. Mena-Enriquez and Carlos Alberto Torres-Cantero
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Jorge A. Brizuela-Mendoza: Exact Sciences and Methodologies Department, University of Guadalajara, Ciudad Guzmán 49000, Mexico
Juan Carlos Mixteco-Sánchez: Natural and Exact Sciences Department, University of Guadalajara, Ameca 46600, Mexico
Maria A. López-Osorio: Natural and Exact Sciences Department, University of Guadalajara, Ameca 46600, Mexico
Gerardo Ortiz-Torres: Computer Science and Engineering Department, University of Guadalajara, Ameca 46600, Mexico
Felipe D. J. Sorcia-Vázquez: Computer Science and Engineering Department, University of Guadalajara, Ameca 46600, Mexico
Ricardo Eliú Lozoya-Ponce: División de Estudios de Posgrado e Investigación, Tecnológico Nacional de México Campus Chihuahua, Chihuahua 31310, Mexico
Moises B. Ramos-Martínez: Computer Science and Engineering Department, University of Guadalajara, Ameca 46600, Mexico
Alan F. Pérez-Vidal: Computer Science and Engineering Department, University of Guadalajara, Ameca 46600, Mexico
Jesse Y. Rumbo Morales: Computer Science and Engineering Department, University of Guadalajara, Ameca 46600, Mexico
Cesar H. Guzmán-Valdivia: Mechatronics Engineering Department, Polytechnic University of Aguascalientes, Aguascalientes 20342, Mexico
Mayra G. Mena-Enriquez: Biomedical Sciences Department, University of Guadalajara, Tonalá 45425, Mexico
Carlos Alberto Torres-Cantero: Tecnológico Nacional de México Campus Colima, Av. Tecnológico # 1, Col. Liberación, Villa de Álvarez 28976, Mexico

Mathematics, 2023, vol. 11, issue 22, 1-19

Abstract: The present paper addresses linear parameter-varying systems with high-order time-varying parameter dependency known as polynomial LPV systems and their controller design. Throughout this work, a procedure ensuring a state-feedback controller from a parameterized linear matrix inequality (PLMI) solution is presented. As the main contribution of this paper, the controller is designed by considering the time-varying parameter rate as a tuning parameter with a continuous control gain in such a way that the closed-loop eigenvalues lie in a complex plane subset, with high-order time-varying parameters defining the system dynamics. Simulation results are presented, aiming to show the effectiveness of the proposed controller design.

Keywords: LMI region; parameterized linear matrix inequalities; polynomial linear parameter varying systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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