Asymptotic unbounded root loci - Formulae and computation
Asymptotic unbounded root loci - Formulae and computation
We study the asymptotic behavior of the dosed loop eigenvalues (root loci) of a strictly proper linear time-invariant control system as loop gain goes to \infty . The formulas are stated in terms of the eigenvalues of nested restricted linear maps of the form A(\mod S_{2})|_{S_{1}} where S 1 and S 2 are subspaces of complementary dimension. Additional geometrical insight into the formulas is obtained by mechanizing the formulas using orthogonal projections. Our method and formulas are useful in other asymptotic calculations as well, e.g., hierarchical multiple-time scales aggregation of Markov chains with some infrequent transitions.
- University of California, Berkeley United States
- Information Systems Laboratories (United States) United States
- Massachusetts Institute of Technology United States
Numerical computation of eigenvalues and eigenvectors of matrices, asymptotic behavior of the closed loop eigenvalues, Eigenvalues, singular values, and eigenvectors, Asymptotic approximations, asymptotic expansions (steepest descent, etc.), Canonical structure, Model systems in control theory, Stability of control systems, Linear systems in control theory, Algebraic methods, Theory of matrix inversion and generalized inverses, Computational methods in systems theory
Numerical computation of eigenvalues and eigenvectors of matrices, asymptotic behavior of the closed loop eigenvalues, Eigenvalues, singular values, and eigenvectors, Asymptotic approximations, asymptotic expansions (steepest descent, etc.), Canonical structure, Model systems in control theory, Stability of control systems, Linear systems in control theory, Algebraic methods, Theory of matrix inversion and generalized inverses, Computational methods in systems theory
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