Coprime Factorizations of Multivariate Rational Matrices

Coprime factorization is a well-known issue in one-dimensional systems theory, having many applications in realization theory, balancing, controller synthesis, etc. Generalization to systems in more than one independent variable is a delicate matter: First, several nonequivalent coprimeness notions for multivariate polynomial matrices have been discussed in the literature: zero, minor, and factor coprimeness. Here we adopt a generalized version of factor primeness that appears to be most suitable for multidimensional systems: a matrix is prime iff it is a minimal annihilator. After reformulating the sheer concept of a factorization, it is shown that every rational matrix possesses left and right coprime factorizations that can be found by means of computer algebraic methods. Several properties of coprime factorizations are given in terms of certain determinantal ideals. Date received: September 10, 1998. Date revised: February 25, 1999.     

Testing controllability and constructibility in discrete linear systems

A simple criterion for complete controllability and constructibility of discrete-time linear constant systems is given in terms of left and right coprimeness of certain polynomial matrices.     

New coprimeness over multivariable polynomial matrices and its application to control delay systems

This paper presents a new notion of coprimeness over multivariable polynomial matrices, where a single variable is given priority over the remaining variables. From a characterization through a set of common zeros of the minors, it is clarified that the presented coprimeness is equivalent to weakly zero coprimeness in the particular variable. An application of the presented coprimeness to control systems with non-commensurate delays and finite spectrum assignment is also presented. Because the presented coprimeness is stronger than minor coprimeness, non-commensurate delays are difficult to deal with in algebraic control theory. The “rational ratio condition” between delays, which can reduce non-commensurate delays to commensurate delays, proves to be both powerful and practical concept in algebraic control theory for delay systems.     

Proper stable Bezout factorizations and feedback control of linear time-delay systems†

This paper deals with the existence and construction of proper stable Bezout factorizations of transfer function matrices of linear time-invariant systems with commensurate time delays. Existence of factorizations is characterized in terms of spectral controllability (or spectral observability)of the co-canonical (or canonical) realization of the transfer function matrix. An explicit procedure for computing proper stable Bezout factorizations is given in terms of a specialized ring of pure and distributed time delays. This procedure is utilized to construct finite-dimensional stabilizing compensators and to construct feedback systems which assign the characteristic polynomial of the closed-loop system.     

Structured system models Part 3. An application to feedback compensator design

The controllability and observability indices are studied and applied to the feedback compensator design. The compensator design method uses polynomial matrices as system models. As the main result, a new algorithm is introduced for the construction of a first candidate for the feedback compensator. A new algorithm is also given for constructing a state-space model from polynomial matrix models. Such a realization is needed if there is originally only a polynomial matrix model for the system.     

广义区间动力系统的能控性

讨论了广义区间动力系统正则性、I-能控与C-能控问题.由于上述问题等价于判别某 个区间矩阵为列满秩,首先得到判别区间矩阵为列满秩的充分条件与充分必要条件,进一步得 到了判别广义区间系统为正则的充分必要条件、I-能控的充分条件与C-能控的充分必要条件. 通过数值实例说明所得到的结果相对于已有结果更具有一般性及有效性.由对偶原理,得到相 应的能观性的判据.