Finite-Time Stability: An Input-Output Approach
Finite-Time Stability: An Input-Output Approach

Author: Francesco Amato

Publisher: John Wiley & Sons

Published: 2018-08-01

Total Pages: 309

ISBN-13: 1119140552

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Systematically presents the input-output finite-time stability (IO-FTS) analysis of dynamical systems, covering issues of analysis, design and robustness The interest in finite-time control has continuously grown in the last fifteen years. This book systematically presents the input-output finite-time stability (IO-FTS) analysis of dynamical systems, with specific reference to linear time-varying systems and hybrid systems. It discusses analysis, design and robustness issues, and includes applications to real world engineering problems. While classical FTS has an important theoretical significance, IO-FTS is a more practical concept, which is more suitable for real engineering applications, the goal of the research on this topic in the coming years. Key features: Includes applications to real world engineering problems. Input-output finite-time stability (IO-FTS) is a practical concept, useful to study the behavior of a dynamical system within a finite interval of time. Computationally tractable conditions are provided that render the technique applicable to time-invariant as well as time varying and impulsive (i.e. switching) systems. The LMIs formulation allows mixing the IO-FTS approach with existing control techniques (e. g. H∞ control, optimal control, pole placement, etc.). This book is essential reading for university researchers as well as post-graduate engineers practicing in the field of robust process control in research centers and industries. Topics dealt with in the book could also be taught at the level of advanced control courses for graduate students in the department of electrical and computer engineering, mechanical engineering, aeronautics and astronautics, and applied mathematics.

Stability of Input/output Dynamical Systems on Metric Spaces
Stability of Input/output Dynamical Systems on Metric Spaces

Author: Hugo Gonzalez Villasanti

Publisher:

Published: 2019

Total Pages: 67

ISBN-13:

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The first part of this dissertation extends the applicability of stability-preserving mappings to dynamical systems whose evolutionary processes explicitly consider the effect of external perturbations (inputs) and measurements (outputs), via multi-valued operators. We provide definitions for input-to-state stability and input-to-output stability for a general class of systems whose trajectories lie in arbitrary metric spaces, indexed by hybrid time sets. Novel proofs of results such as the ISS-Lyapunov and the small-gain theorem are developed with the use of stability-preserving mappings. The second part, where we employ the theory to model and analyze the complex dynamics found in the interplay of the determinants of mood disorders. The model integrates biopsychosocial findings of the bipolar and depressive spectra, modeling attractors corresponding to mood states such as euthymia, mania, depression, the mixed state, anhedonia, hedonia, and flat or blunted affect, as well as the transitions among these attractors caused by external influences, like stress and medication. Conditions for global stability of euthymia, obtained via a stability analysis, are supported by studies in the neuropsychology literature, while computational analyses provide a novel explanation of the mechanism underlying mood stabilizers.

Feedback Systems
Feedback Systems

Author: Charles A. Desoer

Publisher: SIAM

Published: 1975-01-01

Total Pages: 281

ISBN-13: 0898719054

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This book was the first and remains the only book to give a comprehensive treatment of the behavior of linear or nonlinear systems when they are connected in a closed-loop fashion, with the output of one system forming the input of the other. The study of the stability of such systems requires one to draw upon several branches of mathematics but most notably functional analysis. Feedback Systems: Input-Output Properties includes the most basic concepts of matrices and norms, the important fundamental theorems in input-output stability, and the requisite background material in advanced topics such as the small gain theorem and the passivity theorem. Audience: advanced graduate students and researchers in control theory, dynamical systems, and ordinary and partial differential equations.

Nonlinear Dynamical Systems and Control
Nonlinear Dynamical Systems and Control

Author: Wassim M. Haddad

Publisher: Princeton University Press

Published: 2011-09-19

Total Pages: 975

ISBN-13: 1400841046

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Nonlinear Dynamical Systems and Control presents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on Lyapunov-based methods. Dynamical system theory lies at the heart of mathematical sciences and engineering. The application of dynamical systems has crossed interdisciplinary boundaries from chemistry to biochemistry to chemical kinetics, from medicine to biology to population genetics, from economics to sociology to psychology, and from physics to mechanics to engineering. The increasingly complex nature of engineering systems requiring feedback control to obtain a desired system behavior also gives rise to dynamical systems. Wassim Haddad and VijaySekhar Chellaboina provide an exhaustive treatment of nonlinear systems theory and control using the highest standards of exposition and rigor. This graduate-level textbook goes well beyond standard treatments by developing Lyapunov stability theory, partial stability, boundedness, input-to-state stability, input-output stability, finite-time stability, semistability, stability of sets and periodic orbits, and stability theorems via vector Lyapunov functions. A complete and thorough treatment of dissipativity theory, absolute stability theory, stability of feedback systems, optimal control, disturbance rejection control, and robust control for nonlinear dynamical systems is also given. This book is an indispensable resource for applied mathematicians, dynamical systems theorists, control theorists, and engineers.

Stability and Control of Dynamical Systems with Applications
Stability and Control of Dynamical Systems with Applications

Author: Derong Liu

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 459

ISBN-13: 1461200377

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It is with great pleasure that I offer my reflections on Professor Anthony N. Michel's retirement from the University of Notre Dame. I have known Tony since 1984 when he joined the University of Notre Dame's faculty as Chair of the Depart ment of Electrical Engineering. Tony has had a long and outstanding career. As a researcher, he has made im portant contributions in several areas of systems theory and control theory, espe cially stability analysis of large-scale dynamical systems. The numerous awards he received from the professional societies, particularly the Institute of Electrical and Electronics Engineers (IEEE), are a testament to his accomplishments in research. He received the IEEE Control Systems Society's Best Transactions Paper Award (1978), and the IEEE Circuits and Systems Society's Guillemin-Cauer Prize Paper Award (1984) and Myril B. Reed Outstanding Paper Award (1993), among others. In addition, he was a Fulbright Scholar (1992) and received the Alexander von Hum boldt Forschungspreis (Alexander von Humboldt Research Award for Senior U.S. Scientists) from the German government (1997). To date, he has written eight books and published over 150 archival journal papers. Tony is also an effective administrator who inspires high academic standards.

The Analysis of Feedback Systems
The Analysis of Feedback Systems

Author: Jan C. Willems

Publisher: Mit Press

Published: 1970-12-01

Total Pages: 204

ISBN-13: 9780262731607

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This monograph is an attempt to develop further and refine methods based on input -output descriptions for analyzing feedback systems. Contrary to previous work in this area, the treatment heavily emphasizes and exploits the causality of the operators involved. This brings the work into closer contact with the theory of dynamical systems and automata.