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Nonlinear Systems Analysis
Mathukumalli Vidyasagar,Charles A. Desoer +1 more
- 01 Jan 1978
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TL;DR: In this article, the authors consider non-linear differential equations with unique solutions, and prove the Kalman-Yacubovitch Lemma and the Frobenius Theorem.
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Abstract: Introduction. Non-linear Differential Equations. Second-Order Systems. Approximate Analysis Methods. Lyapunov Stability. Input-Output Stability. Differential Geometric Methods. Appendices: Prevalence of Differential Equations with Unique Solutions, Proof of the Kalman-Yacubovitch Lemma and Proof of the Frobenius Theorem.
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Citations
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Linear Matrix Inequalities in System and Control Theory
Edwin E. Yaz
- 01 Jan 1994
TL;DR: In this paper, the authors present a brief history of LMIs in control theory and discuss some of the standard problems involved in LMIs, such as linear matrix inequalities, linear differential inequalities, and matrix problems with analytic solutions.
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A Mathematical Introduction to Robotic Manipulation
Richard M. Murray,S. Shankar Sastry,Li Zexiang +2 more
- 22 Mar 1994
TL;DR: In this paper, the authors present a detailed overview of the history of multifingered hands and dextrous manipulation, and present a mathematical model for steerable and non-driveable hands.
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Stability of Time-Delay Systems
Kequin Gu,Jie Chen,Vladimir L. Kharitonov +2 more
- 26 Jun 2003
TL;DR: Preface, Notations 1.Introduction to Time-Delay Systems I.Robust Stability Analysis II.Input-output stability A.LMI and Quadratic Integral Inequalities Bibliography Index
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Mathematical Control Theory: Deterministic Finite Dimensional Systems
Eduardo D. Sontag
- 01 Jan 1990
TL;DR: This book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects, covering a wide range of topics written in a standard theorem/proof style and develops the necessary techniques from scratch.
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Multiple Lyapunov functions and other analysis tools for switched and hybrid systems
TL;DR: Bendixson's theorem is extended to the case of Lipschitz continuous vector fields, allowing limit cycle analysis of a class of "continuous switched" systems.
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References
•Book
Feedback Systems: Input-output Properties
Charles A. Desoer,Mathukumalli Vidyasagar +1 more
- 01 Jan 1975
TL;DR: In this paper, the Bellman-Gronwall Lemma has been applied to the small gain theorem in the context of linear systems and convolutional neural networks, and it has been shown that it can be applied to linear systems.
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