The main contributions of this paper.
Abstract:
The motivation of this paper comes from the fact that \mathcal {L}_{p}- stability and \mathcal {L}_{p}- gain, using the classical signal norms, is not well-define...Show MoreMetadata
Abstract:
The motivation of this paper comes from the fact that \mathcal {L}_{p}- stability and \mathcal {L}_{p}- gain, using the classical signal norms, is not well-defined for arbitrary continuous weighted homogeneous systems. However, using homogeneous signal norms it is possible to show that every internally stable homogeneous system has a globally defined finite homogeneous \mathcal {L}_{p}- gain, for p sufficiently large. If the system has a homogeneous approximation, the homogeneous \mathcal {L}_{p}- gain is inherited locally. Homogeneous \mathcal {L}_{p}- stability can be characterized by a homogeneous dissipation inequality, which in the input affine case can be transformed to a homogeneous Hamilton-Jacobi inequality. An estimation of an upper bound for the homogeneous \mathcal {L}_{p}- gain can be derived from these inequalities. Homogeneous \mathcal {L}_{\infty }- stability is also considered and its strong relationship to Input-to-State stability is studied. These results are extensions to arbitrary homogeneous systems of the well-known situation for linear time-invariant systems, where the Hamilton-Jacobi inequality reduces to an algebraic Riccati inequality. A natural application of finite-gain homogeneous \mathcal {L}_{p}- stability is in the study of stability for interconnected systems. An extension of the small-gain theorem for negative feedback systems and results for systems in cascade are derived for different homogeneous norms. Previous results in the literature use classical signal norms, hence, they can only be applied to a restricted class of homogeneous systems. The results are illustrated by several examples.
The main contributions of this paper.
Published in: IEEE Access ( Volume: 10)
Funding Agency:
Control Engineering Group, Technische Universität Ilmenau, Ilmenau, Germany
Daipeng Zhang was born in Anshan, Liaoning, China, in 1986. He received the B.S. degree in automation and electrical engineering from Zhejiang University, Hangzhou, China, in 2008, and the M.S. degree in control theory and electrical engineering from the University of Southern California, Los Angeles, USA, in 2010. He is currently pursuing the Ph.D. degree with the Control Engineering Group, Technische Universität Ilmenau...Show More
Daipeng Zhang was born in Anshan, Liaoning, China, in 1986. He received the B.S. degree in automation and electrical engineering from Zhejiang University, Hangzhou, China, in 2008, and the M.S. degree in control theory and electrical engineering from the University of Southern California, Los Angeles, USA, in 2010. He is currently pursuing the Ph.D. degree with the Control Engineering Group, Technische Universität Ilmenau...View more
Instituto de Ingeniería, Universidad Nacional Autónoma de México, Ciudad de México, Mexico
Jaime A. Moreno (Member, IEEE) was born in Colombia. He received the Licentiate degree (Hons.) in electronic engineering from the Universidad Pontificia Bolivariana, Medellín, Colombia, in 1987, the Diplom degree in electrical engineering (automatic control) from the Universität zu Karlsruhe, Karlsruhe, Germany, in 1990, and the Ph.D. degree (summa cum laude) in electrical engineering (automatic control) from the Helmut-S...Show More
Jaime A. Moreno (Member, IEEE) was born in Colombia. He received the Licentiate degree (Hons.) in electronic engineering from the Universidad Pontificia Bolivariana, Medellín, Colombia, in 1987, the Diplom degree in electrical engineering (automatic control) from the Universität zu Karlsruhe, Karlsruhe, Germany, in 1990, and the Ph.D. degree (summa cum laude) in electrical engineering (automatic control) from the Helmut-S...View more
Control Engineering Group, Technische Universität Ilmenau, Ilmenau, Germany
Johann Reger (Senior Member, IEEE) received the Diploma degree (Dipl.-Ing.) in mechanical engineering and the Dr.-Ing. degree in control engineering from the University of Erlangen-Nuremberg, Germany, in 1999 and 2004, respectively. He has held several postdoctoral positions, among others, with the Mechatronics Department, CINVESTAV-IPN, Mexico City; the EECS Control Laboratory, University of Michigan, Ann Arbor; and the ...Show More
Johann Reger (Senior Member, IEEE) received the Diploma degree (Dipl.-Ing.) in mechanical engineering and the Dr.-Ing. degree in control engineering from the University of Erlangen-Nuremberg, Germany, in 1999 and 2004, respectively. He has held several postdoctoral positions, among others, with the Mechatronics Department, CINVESTAV-IPN, Mexico City; the EECS Control Laboratory, University of Michigan, Ann Arbor; and the ...View more
Contents Control Engineering Group, Technische Universität Ilmenau, Ilmenau, Germany
Daipeng Zhang was born in Anshan, Liaoning, China, in 1986. He received the B.S. degree in automation and electrical engineering from Zhejiang University, Hangzhou, China, in 2008, and the M.S. degree in control theory and electrical engineering from the University of Southern California, Los Angeles, USA, in 2010. He is currently pursuing the Ph.D. degree with the Control Engineering Group, Technische Universität Ilmenau, Ilmenau, Germany. His research interest includes the revision and application of finite-gain Lp– stability on continuous homogeneous systems.
Daipeng Zhang was born in Anshan, Liaoning, China, in 1986. He received the B.S. degree in automation and electrical engineering from Zhejiang University, Hangzhou, China, in 2008, and the M.S. degree in control theory and electrical engineering from the University of Southern California, Los Angeles, USA, in 2010. He is currently pursuing the Ph.D. degree with the Control Engineering Group, Technische Universität Ilmenau, Ilmenau, Germany. His research interest includes the revision and application of finite-gain Lp– stability on continuous homogeneous systems.View more
Instituto de Ingeniería, Universidad Nacional Autónoma de México, Ciudad de México, Mexico
Jaime A. Moreno (Member, IEEE) was born in Colombia. He received the Licentiate degree (Hons.) in electronic engineering from the Universidad Pontificia Bolivariana, Medellín, Colombia, in 1987, the Diplom degree in electrical engineering (automatic control) from the Universität zu Karlsruhe, Karlsruhe, Germany, in 1990, and the Ph.D. degree (summa cum laude) in electrical engineering (automatic control) from the Helmut-Schmidt University, Hamburg, Germany, in 1995. He is currently a Full Professor of automatic control and the Head of the Electrical and Computing Department, Institute of Engineering, National Autonomous University of Mexico (UNAM), Mexico City. He is the author and an editor of eight books, 12 book chapters, one patent, and authored or coauthored of more than 450 articles in refereed journals and conference proceedings. His current research interests include robust and nonlinear control, in particular, with emphasis on Lyapunov methods for higher order sliding mode control, with applications to biochemical (wastewater treatment processes) and electromechanical processes, and the design of nonlinear observers. He is a member of the IFAC Council.
Jaime A. Moreno (Member, IEEE) was born in Colombia. He received the Licentiate degree (Hons.) in electronic engineering from the Universidad Pontificia Bolivariana, Medellín, Colombia, in 1987, the Diplom degree in electrical engineering (automatic control) from the Universität zu Karlsruhe, Karlsruhe, Germany, in 1990, and the Ph.D. degree (summa cum laude) in electrical engineering (automatic control) from the Helmut-Schmidt University, Hamburg, Germany, in 1995. He is currently a Full Professor of automatic control and the Head of the Electrical and Computing Department, Institute of Engineering, National Autonomous University of Mexico (UNAM), Mexico City. He is the author and an editor of eight books, 12 book chapters, one patent, and authored or coauthored of more than 450 articles in refereed journals and conference proceedings. His current research interests include robust and nonlinear control, in particular, with emphasis on Lyapunov methods for higher order sliding mode control, with applications to biochemical (wastewater treatment processes) and electromechanical processes, and the design of nonlinear observers. He is a member of the IFAC Council.View more
Control Engineering Group, Technische Universität Ilmenau, Ilmenau, Germany
Johann Reger (Senior Member, IEEE) received the Diploma degree (Dipl.-Ing.) in mechanical engineering and the Dr.-Ing. degree in control engineering from the University of Erlangen-Nuremberg, Germany, in 1999 and 2004, respectively. He has held several postdoctoral positions, among others, with the Mechatronics Department, CINVESTAV-IPN, Mexico City; the EECS Control Laboratory, University of Michigan, Ann Arbor; and the Control Systems Group, TU Berlin. Since 2008, he has been a Full Professor and the Head of the Control Engineering Group, Computer Science and Automation Faculty, TU Ilmenau, Germany. There, he also serves as the Vice-Dean and the Director of the Institute for Automation and Systems Engineering. His current research interests include adaptive and robust control, variable structure, and sliding mode control, state, and parameter estimation. His application areas include robotics, mechatronics, automotive, and water systems.
Johann Reger (Senior Member, IEEE) received the Diploma degree (Dipl.-Ing.) in mechanical engineering and the Dr.-Ing. degree in control engineering from the University of Erlangen-Nuremberg, Germany, in 1999 and 2004, respectively. He has held several postdoctoral positions, among others, with the Mechatronics Department, CINVESTAV-IPN, Mexico City; the EECS Control Laboratory, University of Michigan, Ann Arbor; and the Control Systems Group, TU Berlin. Since 2008, he has been a Full Professor and the Head of the Control Engineering Group, Computer Science and Automation Faculty, TU Ilmenau, Germany. There, he also serves as the Vice-Dean and the Director of the Institute for Automation and Systems Engineering. His current research interests include adaptive and robust control, variable structure, and sliding mode control, state, and parameter estimation. His application areas include robotics, mechatronics, automotive, and water systems.View more