Controller synthesis for switched T–S fuzzy positive systems described by the Fornasini–Marchesini second model

Abstract In this paper, controller synthesis problem is investigated for a class of Fornasini–Marchesini second type switched systems with time-varying delays under the Takagi–Sugeno fuzzy rules. Both the cases of state feedback controller and static output feedback controller are designed. By utilizing the common Lyapunov function approach and the multiple Lyapunov functions method, sufficient criteria are derived in the form of linear matrix inequalities to assure the resulting closed-loop 2-D systems to be positive and asymptotically stable, which can be easily computed using the existing numerical algorithms. Explicit design schemes for the state feedback/static output feedback controllers gain matrices are also presented. Finally, advantage and effectiveness of the proposed criteria are shown by a numerical example.

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