Control of fractional order chaotic system via Hermit eigenvalue analysis

In this brief paper, some new results for stability analysis of fractional order time variant ordinary differential systems (ODEs) are given. These results are directly extended based on related results of commensurate integer order ODEs, which were always ignored by some researchers in the research field of fractional dynamics analysis. Main results are proved to be right via stability region analysis, since the stability region of a commensurate fractional order system must be much larger than that of a integral order one. Based on our main theoretical results, one can design practical control scheme for some fractional dynamical system. Our theoretical analysis corrected some existing wrong usage of eigenvalue analysis method on dynamics of time variant ordinary differential systems. Finally, by taking the fractional Lorenz chaotic system as an example, a simple linear feedback control strategy is designed for stabilizing the the states of the Lorenz system by adjusting only one key control parameter according to the Hermit eigenvalues analysis results. Numerical results show the rightness of the theoretical analysis.