Estimating distances from quadruples satisfying stability properties to quadruples not satisfying them
Copyright policy )Estimating distances from quadruples satisfying stability properties to quadruples not satisfying them
We consider quadruples of matrices (E,A,B,C) defining generalized linear multivariable time-invariant dynamical systems, with E,A square matrices and B, C rectangular matrices. Using geometrical techniques we present upper bounds and lower bounds for the distances between a quadruple and the nearest structurally unstable, uncontrollable and/or unobservable one, in terms of the singular values of matrices associated to the quadruple.
- Universitat Polite`cnica de Catalunya Spain
- ETSEIB Spain
- Universitat Politècnica de Catalunya Spain
Differential equations, Eigenvalues, singular values, and eigenvectors, observability, Sistemes, Control::93B Controllability, Classificació AMS::34 Ordinary differential equations::34D Stability theory, Control::93B Controllability, observability, and system structure, differential-algebraic equations, controllability, Structural stability and analogous concepts of solutions to ordinary differential equations, :34 Ordinary differential equations::34A General theory [Classificació AMS], Discrete Mathematics and Combinatorics, Time-invariant (generalized) linear dynamical systems, Equacions diferencials ordinàries, Sistemes, Teoria de, Classificació AMS::93 Systems Theory; Control::93B Controllability, observability, and system structure, System theory, distance of quadruples of matrices, Numerical Analysis, :93 Systems Theory [Classificació AMS], Algebra and Number Theory, Teoria de, upper and lower bounds, and system structure, :93B Controllability, observability, and system structure [Control], Classificació AMS::93 Systems Theory, Linear systems in control theory, Algebraic methods, structural stability, Geometry and Topology, Classificació AMS::34 Ordinary differential equations::34A General theory, Implicit ordinary differential equations, differential-algebraic equations, Control problems involving ordinary differential equations, :34 Ordinary differential equations::34D Stability theory [Classificació AMS]
Differential equations, Eigenvalues, singular values, and eigenvectors, observability, Sistemes, Control::93B Controllability, Classificació AMS::34 Ordinary differential equations::34D Stability theory, Control::93B Controllability, observability, and system structure, differential-algebraic equations, controllability, Structural stability and analogous concepts of solutions to ordinary differential equations, :34 Ordinary differential equations::34A General theory [Classificació AMS], Discrete Mathematics and Combinatorics, Time-invariant (generalized) linear dynamical systems, Equacions diferencials ordinàries, Sistemes, Teoria de, Classificació AMS::93 Systems Theory; Control::93B Controllability, observability, and system structure, System theory, distance of quadruples of matrices, Numerical Analysis, :93 Systems Theory [Classificació AMS], Algebra and Number Theory, Teoria de, upper and lower bounds, and system structure, :93B Controllability, observability, and system structure [Control], Classificació AMS::93 Systems Theory, Linear systems in control theory, Algebraic methods, structural stability, Geometry and Topology, Classificació AMS::34 Ordinary differential equations::34A General theory, Implicit ordinary differential equations, differential-algebraic equations, Control problems involving ordinary differential equations, :34 Ordinary differential equations::34D Stability theory [Classificació AMS]
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