.2-d Discrete System Stability

During the past years a great deal of interest has been devoted to the study of two-dimensional (2-D) linear discrete systems due to their applications in engineering and physics, and a great number of notions and results in one-dimensional state-space systems have been extended to 2-D systems. In recent research on 2-D systems, we have gained abundant valuable results, which provide us with profound academic basis for the farther research on 2-D discrete systems. In the light of recent work in the theory of 2-D discrete system, this dissertation provides a systematic study on the theory of 2-D singular systems and a set of 2-D discrete systems with plural coefficient, and some new notions are proposed. The main contents and results in this dissertation are as follows:We introduce the models of 2-D singular systems. And we present some important quality of the systems.We focus on the stability of 2-D singular systems. First, based on the existing results of stability of 2-D SGM, the asymptotic stability and exponential stability concept of the 2-D acceptable system is extended to the 2-D singular case. We discuss the relationship between the asymptotic stability and stability test polynomial. The sufficient and necessary conditions for stabilizability and detectability of 2-D singular systems are obtained respectively, and the relationship between BIBO stability and asymptotic stability is discussed based on these conditions.We describe a set of 2-D discrete systems with plural coefficient and find a new solution to the stability of these systems. We employ Fourier techniques and the Mean Ergodic Theorem to prove the stability.Finally, we point out the insufficiency about this thesis and propose some problems that need to be solved further and prospect the development of 2-D discrete systems.