Frequency-distributed representation of irrational linear systems

Abstract

Abstract The present work extends and generalizes the notion of frequency-distributed (FD) representation to a broad class of linear, stationary, continuous-time systems. On one hand, the proposed FD representation can be seen as a generalization of the diffusive representation, which is primarily utilized in the context of fractional order systems. Alternatively, it can also be seen as an extension to the Jordan canonical form, which is used as one of the main theoretical tools when analyzing finite-dimensional systems. Sufficient conditions under which FD representation can be achieved are derived. The proposed approach ensures real-valued state functions and output weights even when applied to oscillatory systems, and in a wast majority of cases manages to avoid utilization of generalized functions. Potential applications include simulation, representation theory and stability analysis, control synthesis, etc. All considerations have been illustrated by numerical examples.