Two-dimensional linear discrete systems: a polynomial fractional approach



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Texas Tech University


The purpose of this dissertation is two-fold. First, the class of two-dimensional linear time-invariant discrete system is investigated and a unified approach is proposed for its representation. This approach based on the two-dimensional polynomial fractional representation is further extended to two-dimensional, linear, time-varying discrete systems. This algebraic framework is established with use of the division process in K[z1,z2] which is defined and investigated. Also, a ring of generalized two-dimensional polynomials K{z1-,z2} with the division property is defined.

The main structure of the proposed realization and control theory is based on a module of signals over a two-dimensional polynomial ring and a skew polynomial ring.

The 2-D Kalman input-output map is defined and realization based on its factorization is considered. Also, various models for 2-D systems are considered for the time-invariant case.

Secondly, system-theoretic properties such as reachability and observability are explored. The stability problem is considered. In a sequel the polynomial equation Q X + R Y = ö is explored. The conditions are specified for control of two-dimensional systems.



Discrete-time systems, Polynomial rings, Control theory, Time-series analysis