Trends in Multidimensional Systems Theory

Abstract

The theories of functions and polynomials of several complex and/or real variables along with their numerous applications in several areas of systems theory primarily concerned with the topics of multidimensional digital filter stability, stabilization and design, multivariate network realizability theory, digital array processing in the general framework of multidimensional signal processing techniques needed to process signals carried by propagating wave phenomena, in addition to problems occurring in control theory concerned with 2-D state-space models, notions of controllability, observability, minimality, feedback and pole-placement as well as stabilization via output feedback provided the subject matter of a Special Issue devoted to Multidimensional Systems [1]. Though the vast majority of the papers in [1] were concerned with multidimensional deterministic systems, a paper concerned with methods for inference about models of random processes on multidimensional Euclidean space from observed data was also included especially because the mathematical tools employed partially fitted those widely used in the Issue and also because it was felt at that time that the future scopes for development of multidimensional systems theory should not be restricted to deterministic systems only. In fact, broadly speaking, multidimensional systems theory spans deterministic and statistical approaches to the modeling, analysis and design of spatio-temporal continuous and discrete systems.