Stability theory

Massera's lemma

In stability theory and nonlinear control, Massera's lemma, named after José Luis Massera, deals with the construction of the Lyapunov function to prove the stability of a dynamical system. The lemma appears in as the first lemma in section 12, and in more general form in as lemma 2. In 2004, Massera's original lemma for single variable functions was extended to the multivariable case, and the resulting lemma was used to prove the stability of switched dynamical systems, where a common Lyapunov function describes the stability of multiple modes and switching signals. (Wikipedia).

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Proof of Lemma and Lagrange's Theorem

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof of Lemma and Lagrange's Theorem. This video starts by proving that any two right cosets have the same cardinality. Then we prove Lagrange's Theorem which says that if H is a subgroup of a finite group G then the order of H div

From playlist Abstract Algebra

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Burnside's Lemma (Part 2) - combining math, science and music

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From playlist Traditional topics, explained in a new way

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Beltrami Identity Derivation

The Beltrami Identity is a necessary condition for the Euler-Lagrange equation (so if it solves the E-L equation, it solves the Beltrami identity). Here it is derived from the total derivative of the integrand (e.g. Lagrangian).

From playlist Physics

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Lagrange Multipliers: Abs Extrema of Paraboloid Under Circular Constraint

This video provides and example of how to use the method of Lagrange Multipliers.

From playlist Lagrange Multipliers

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Set Theory (Part 2): ZFC Axioms

Please feel free to leave comments/questions on the video and practice problems below! In this video, I introduce some common axioms in set theory using the Zermelo-Fraenkel w/ choice (ZFC) system. Five out of nine ZFC axioms are covered and the remaining four will be introduced in their

From playlist Set Theory by Mathoma

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From playlist Physics

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Theory of numbers: Gauss's lemma

This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di

From playlist Theory of numbers

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This lecture is part of an online course on the Zermelo Fraenkel axioms of set theory. This lecture gives an overview of the axioms, describes the von Neumann hierarchy, and sketches several approaches to interpreting the axioms (Platonism, von Neumann hierarchy, multiverse, formalism, pra

From playlist Zermelo Fraenkel axioms

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From playlist Mathematics

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Lagrange Multipliers Maximum of f(x, y, z) = xyz subject to x + y + z - 3 = 0

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From playlist Calculus 3

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Graph regularity and counting lemmas - Jacob Fox

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From playlist Mathematics

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Regularity methods in combinatorics, number theory, and computer science - Jacob Fox

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From playlist Mathematics

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9. Szemerédi's graph regularity lemma IV: induced removal lemma

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From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019

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6. Szemerédi's graph regularity lemma I: statement and proof

MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Szemerédi's graph regularity lemma is a powerful tool in

From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019

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A stable arithmetic regularity lemma in finite (...) - C. Terry - Workshop 1 - CEB T1 2018

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From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields

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7. Szemerédi's graph regularity lemma II: triangle removal lemma

MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Continuing the discussion of Szemerédi's graph regularity

From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019

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László Lovász: The many facets of the Regularity Lemma

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From playlist Abel Lectures

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10. Szemerédi's graph regularity lemma V: hypergraph removal and spectral proof

MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX In this first half of this lecture, Prof. Zhao shows how

From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019

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15. Graph limits II: regularity and counting

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From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019

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Multivariable Calculus | Lagrange multipliers

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From playlist Multivariable Calculus

Related pages

José Luis Massera | Dynamical system | Nonlinear control | Lyapunov function | Stability theory