Control of a Novel Chaotic Fractional Order System Using a State Feedback Technique

TL;DR

This paper introduces a new fractional order chaotic system, analyzes its stability, and proposes a simple scalar feedback control method to stabilize its equilibrium points, confirmed by numerical simulations.

Contribution

It presents a novel fractional order chaotic system and a straightforward control approach that outperforms existing nonlinear methods in simplicity and effectiveness.

Findings

Chaos exists for system orders less than three

Derived stability conditions using Routh-Hurwitz and Matignon criteria

Numerical simulations confirm theoretical stability results

Abstract

We consider a new fractional order chaotic system displaying an interesting behavior. A necessary condition for the system to remain chaotic is derived. It is found that chaos exists in the system with order less than three. Using the Routh-Hurwitz and the Matignon stability criteria, we analyze the novel chaotic fractional order system and propose a control methodology that is better than the nonlinear counterparts available in the literature, in the sense of simplicity of implementation and analysis. A scalar control input that excites only one of the states is proposed, and sufficient conditions for the controller gain to stabilize the unstable equilibrium points derived. Numerical simulations confirm the theoretical analysis.