Yih T. Tsay

Transformations of a class of multivariable control systems to block companion forms

Similarity block transformations are developed to transform a class of linear time-invariant MIMO state equations in arbitrary coordinates into block companion forms so that the classical lines of thought for SISO systems can be extended to MIMO systems.

A fast method for computing the principal nth roots of complex matrices

Abstract Based on the generalized continued-fraction method for finding the nth roots of real numbers, this paper presents a fast computation method for finding the principal nth roots of complex matrices. Computation algorithms with high convergence rates are developed, and their global convergence properties are investigated from the viewpoint of systems theory.

Block-Diagonalization and Block-Triangularization of a Matrix via the Matrix Sign Function.

Abstract A matrix sign function in conjunction with a geometric approach is utilized to construct a block modal matrix and a (scalar) modal matrix of a system map, so that the system map can be block-diagonalized and block-triangularized, and that the Riccati-type problems can be solved.

State-feedback decomposition of multivariable systems via block-pole placement

Some recently developed algebraic theorems of λ-matrices and applications to matrix fraction descriptions of a class of multivariable systems are introduced. Also, a new block-pole placement is developed for the state-feedback block decomposition of multivariable systems.

Block partial fraction expansion of a rational matrix

The main contribution. is a block partial fraction expansion of a rational matrix are polynomial matrices. A new algorithm is derived to construct a transformation matrix that transforms a right (left) solvent to the corresponding left (right) solvent of a matrix polynomial. Also, the algorithm can be used to construct a set of right (left) fundamental matrix polynomials and the inversion of a block Vandermonde matrix. This leads to a new technique to perform the block partial fraction expansion of a class of rational matrices.

Computation of the principal nth roots of complex matrices

A new computational algorithm for finding the principal n th roots and associated roots of complex matrices is developed via a recursive solution of a block discrete state equation.

Multivariable state-feedback self-tuning controllers ∗

This paper describes a state-space approach for self-tuning control of a class of multivariable stochastic systems having the same number of inputs as outputs. A multivariable state-feedback self-tuning controller, based on pole-assignment concepts, is derived. The developed multivariable self-tuner can be applied to stable/unstable and minimum/non-minimum phase linear time-invariant multivariable systems. A multivariable reduced-order self-tuner and a state-feedback minimum-variance self-tuner are also derived. The simplicity and flexibility of the proposed state-space approach facilitate the practical applications of self-tuning control concepts to real systems

Transformations of Solvents and Spectral Factors of Matrix Polynomials, and their Applications,

The relationships between solvents and spectral factors of a high-degree matrix polynomial are explored. Various new transformations are developed to convert right (left) solvents into spectral factors and vice versa. The transformation of a right (left) solvent to a left (right) solvent is also established. The newly established algorithms are then applied to determine the spectral factorization of a matrix polynomial for optimal control problems. The developed algebraic theory enhances the capability of the analysis and synthesis of a system described by a high-degree matrix differential equation.

A squared magnitude continued fraction expansion for stable reduced models

The direct continued fraction method of model reduction for single-input-output and multi-input—output cases sometimes produces unstable reduced models. A generalization is made by using the squared magnitude continued fraction and factorization technique to obtain reduced models which are always stable.

Algorithms for solvents and spectral factors of matrix polynomials

A generalized Newton method, based on the contracted gradient of a matrix polynomial, is derived for solving the right (left) solvents and spectral factors of matrix polynomials. Two methods of selecting initial estimates for rapid convergence of the newly developed numerical method are proposed. Also, new algorithms for solving complete sets of the right (left) solvents and spectral factors without directly using the eigenvalues of matrix polynomials are derived. The proposed computer-aided method can be used to determine the spectral factorization of a matrix polynomial for optimal control, filtering and estimation problems.