Cartanian Geometry, Nonlinear Waves, and Control Theory, Part 1 |
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Common terms and phrases
A₁ A₂ algebraic geometry applied Bäcklund transformation Cartan classical coefficients commutative complex numbers Consider control theory coordinates coset space defined denote derivatives differential forms differential geometry dx dt eigenvalues element exp(ta exterior differential system fiber finite dimensional formula functions Grassmann Grassmann manifold Hamiltonian Hence Hermann holomorphic input system input-output relations input-output system integral invariant isospectral isospectral deformation kernel Korteweg-de Vries Let G Lie algebra Lie group Lie system Lie theory linear differential operator linear maps linear subspace linear systems manifold Math matrix Riccati equations nonlinear notation one-forms one-parameter pair parameter polynomial problem properties Riccati equation Riemann satisfied scalar solutions structure subalgebra subgroup of G subset Suppose symplectic systems theory tangent Theorem time-varying time-varying systems transformation group V₁ variables vector bundle vector fields vector space zero Λω στ
Popular passages
Page 102 - Applications of Algebraic Geometry to Systems Theory, Part II: Feedback and Pole Placement for Linear Hamiltonian Systems", Proceedings IEEE 65 (1977), 841-848.
Page 500 - L. Ljung, T. Kailath and B. Friedlander, "Scattering Theory and Linear Least Squares Estimation, Part I : Continuous-Time Problems", Proc.
Page 317 - Prove that every vector can be written in a unique way as a linear combination of a fixed basis.
Page 453 - ^ is a generating subalgebra if it contains the unit element and if every element of 2* can be written as a linear combination of elements of the form a...
Page 52 - Sup. (3) 74 (1957), 85-177. 2. S. Helgason, Differential geometry and symmetric spaces. Academic Press, New York, 1962. 3.
Page 4 - ... we shall assume that the reader is familiar with the rudiments of manifold and Lie group theory [1,19,20,28,29].
Page 80 - WA Coppel, Matrix quadratic equations, Bull. Austral. Math. Soc. 10 (1974) 377-401.
Page 24 - Manifolds and Global Properties of the Riccati Equation" , Proceedings of the International Symposium on Operator Theory of Networks and Systems, Vol. 2, August 17-19, 1977, Lubbock, Texas, pp. 82-85. 6. R. Hermann and C. Martin, "Lie Theoretic Aspects of the Riccati Equation", Proceedings of the 1977 CDC Conference, New Orleans, La.
Page 24 - Grassmannian Manifolds, Riccati Equations and Feedback Invariants of Linear Systems," in Geometrical Methods for the Theory of Linear Systems (ed. C. Byrnes and C. Martin), Reidel, Dordrecht, 1980. 3. CR Schneider, "Global Aspects of the Matrix Riccati Equation,
Page 396 - Every element of A can be written (in at least one way) as a sum of elements of A