Fractional-Order State Space Models

TL;DR

This paper explores alternative mathematical descriptions and solution methods for fractional-order dynamical systems in state space, highlighting differences from integer-order systems and discussing control implications with simulation results.

Contribution

It introduces new approaches to modeling fractional-order systems in state space and emphasizes the importance of initialization functions and control theory adaptations.

Findings

Fractional-order systems require different state space representations.

Initialization functions are crucial for fractional-order system solutions.

Simulation results validate the proposed methods.

Abstract

In this paper we will present some alternative types of mathematical description and methods of solution of the fractional-order dynamical system in the state space. We point out the difference in the true sense of the name "state" space for the integer-order and fractional-order system and the importance of the initialization function for the fractional-order system. Some implications concerning the state feedback control theory are discussed. Presented are the results of simulations.