Design of fuzzy state feedback controller for robust stabilization of uncertain fractional-order chaotic systems

Abstract

In this paper, the stabilization problem of uncertain fractional-order chaotic systems is investigated in the case where the fractional order α satisfies 0<α<1 and 1≤α<2. Firstly, the uncertain fractional-order chaotic system is described by the so-called fractional-order T–S fuzzy model, and then the fuzzy state feedback controller is correspondingly designed. Secondly, sufficient conditions are derived for the robust asymptotical stability of the closed-loop control systems in those two cases. These criteria are expressed in terms of linear matrix inequalities (LMIs), and the feedback gain matrices can be formulated into the solvability of the relevant LMIs. The proposed controller overcomes some defects in traditional control techniques and is easy to implement. Finally, two numerical examples are presented to demonstrate the effectiveness and the feasibility of the robust stabilizing controller and the robust asymptotical stability criteria.