On Chebyshev systems and non-uniform sampling related to controllability and observability of caputo fractional differential systems

TL;DR

This paper investigates the controllability and observability of Caputo fractional differential systems of any real order, utilizing Chebyshev systems to analyze their properties and extend results to non-uniform sampling scenarios.

Contribution

It introduces a novel approach using Chebyshev systems to analyze controllability and observability of fractional systems and extends these results to non-uniform sampling cases.

Findings

Controllability and observability are characterized via Chebyshev systems.

Extensions to non-uniform sampling are established.

Sampling instants can be chosen freely without restrictions due to Chebyshev properties.

Abstract

This paper is concerned with the investigation of the controllability and observability of Caputo fractional differential linear systems of any real order {\alpha} . Expressions for the expansions of the evolution operators in powers of the matrix of dynamics are first obtained. Sets of linearly independent continuous functions or matrix functions, which are also Chebyshev systems, appear in such expansions in a natural way. Based on the properties of such functions, the controllability and observability of the Caputo fractional differential system of real order {\alpha} are discussed as related to their counterpart properties in the corresponding standard system defined for {\alpha} = 1. Extensions are given to the fulfilment of those properties under non- uniform sampling. It is proved that the choice of the appropriate sampling instants ion not restrictive as a result of the properties of the associate Chebyshev systems