We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Structural Spectral Methods for Solving Continuous Lyapunov Equations.
- Authors
Yadykin, I. B.; Galyaev, I. A.
- Abstract
For linear multivariable continuous stationary stable control systems with a simple spectrum, presented in the form of a canonical diagonal form, controllability and observability forms, a method was developed and analytical formulas for spectral decompositions of gramians in the form of various Xiao matrices were obtained. A method and algorithm for calculating generalized Xiao matrices in the form of the Hadamard product for multiply connected continuous linear systems with many inputs and many outputs have been developed. This allows us to calculate the elements of the corresponding controllability and observability gramians in the form of products of the corresponding elements of the multiplier matrices and a matrix that is the sum of all possible products of the numerator matrices of the matrix transfer function of the system. New results are obtained in the form of spectral and singular decompositions of the inverse gramians of controllability and observability. This makes it possible to obtain invariant decompositions of energy functionals and formulate new criteria for the stability of linear systems taking into account the nonlinear effects of mode interaction.
- Subjects
STABILITY of linear systems; HADAMARD matrices; EQUATIONS; TRANSFER functions; MATRIX multiplications
- Publication
Automation & Remote Control, 2023, Vol 84, Issue 12, p1259
- ISSN
0005-1179
- Publication type
Article
- DOI
10.1134/S0005117923120081