Discrete time convolution control systems

Abstract

In this paper, we study a general class of linear time invariant discrete time distributed systems. We consider both single-input-single-output (SISO) and multi-input-multi-output (MIMO) systems, and study design procedures. We develop a commutative algebra of transfer function, b(p0), for a general class of SISO discrete time convolution systems, which covers sampled distributed systems and, of course, lumped systems as a special case. Each element of b(p0) is formulated as a ratio of two elements in an algebra l1−(p0) of causal p0-stable transfer functions. We demonstrate that l1−(p0) indeed a euclidean ring, give necessary and sufficient conditions for coprimeness between elements in l1−(p0) and characterize poles and zeros for elements in b(p0). In contrast to the algebra l1 the algebra b(p0) includes both stable and unstable systems; furthermore since p0<1 this formulation allows us to study the dominant poles inside the unit disc of the complex plane. We study next MIMO systems whose transfer functi...