Generalized Lyapunov stability and designing pseudo-state/order estimator for incommensurate variable order systems

Abstract

This paper aims to develop a framework for estimating the order and pseudo-state of incommensurate variable order systems, simultaneously. First, some lemmas and theorems are proposed investigating the stability of systems having variable order of derivation. Afterward, multivariable systems with incommensurate variable order are considered and a method is proposed to estimate their pseudo-state and order vectors. The platform provided in this paper facilitates the direct extension of the traditional methods to mainstream dynamical systems, i.e., the multivariable systems with incommensurate variable order, in the sense that other dynamical systems can be considered as simplified versions of such systems.