Decentralised robust H∞ control of fractional-order interconnected systems with uncertainties

The decentralied robust H control problem is considered for fractional-order interconnected systems subject to time-invariant norm-bounded uncertainties in the system, control input and interconnection matrices. First, sufficient conditions for designing a decentralised robust H state feedback controller to guarantee that the closed-loop fractional-order interconnected systems are asymptotically stable with prescribed H performance for all admissible uncertainties are given in terms of linear matrix inequalities. Second, a convex optimisation problem with linear matrix inequality constraints is formulated to design a decentralised robust H state feedback controller with lower gains. Finally, one illustrative example is given to demonstrate the effectiveness of the proposed theoretical results.