Computations, Properties and Applications of Matrix-Valued Functions to Mathematical Science and Control Systems
Abstract
A complete study of the principal nth root of a complex matrix and associated matrix-valued functions is presented in this research report. The principal nth root of a matrix is shown to be useful for the following: constructing the matrix-sign function and the (generalized) matrix-sector function; solving the matrix Lyapunov and Riccati equations; separating matrix eigenvalues relative to a circle, sector and a sector of a circle in the lambda- plane; block-diagonalization (parallel decomposition) and block- triangularization (cascaded decomposition) of a general system matrix; generalizing the block-partial-fraction expansion of a rational matrix; and modelling a continuous-time system from the identified discrete-time model. Also, in this research report, new definitions and computational algorithms have been presented to determine the rectangular and polar representations of a complex matrix. Furthermore, their applications to control systems have been discussed. Finally, utilizing the developed algorithms, a multi-stage design procedure has been established to design discrete-time controllers to achieve pole-assignment in a specified region for a large-scale discrete-time multivariable system.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1991
- Accession Number
- ADA232448
Entities
People
- Leang S. Shieh
Organizations
- University of Houston