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

ABSTRACT

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.

Keywords:

• Decentralised control
• fractional-order system
• H_∞ control
• interconnected system
• robust stability
• robust stabilisation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China [grant number 60974002], [grant number 61374030], [grant number 61533012].