Stability analysis of a discrete-time system with a variable-, fractional-order controller

摘要

Variable, fractional-order backward difference is a generalisation of commonly known difference or sum. Equations with these differences can be used to describe a variable-, fractional order digital control strategies. One should mention, that classical tools such as a state-space description and discrete transfer function cannot be used in the analysis and synthesis of such a type of systems. Equations describing a closed-loop system are proposed. They contain square matrices imitating the action of matrices in the system polynomial matrix description. This paper focuses on the stability analysis of a closed-loop SISO linear system with a controller described by the equations mentioned. A stability condition based on a transient denominator matrix condition number is proposed. Investigations are supported by two numerical examples.