Distributed control of time-delay interconnected nonlinear systems |
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| Institution: | 1. Federal University of Minas Gerais, Graduate Program in Electrical Engineering, Av. Antonio Carlos, 6627, Belo Horizonte, MG 31270-901, Brazil;2. Federal University of Minas Gerais, Department of Electronics Engineering, Av. Antonio Carlos, 6627, Belo Horizonte, MG 31270-901, Brazil;3. Federal University of São João del-Rei, Department of Electrical Engineering, Praça Frei Orlando, 170, São João del-Rei, MG, Brazil;1. School of Mechanical and Precision Instrument Engineering, Xi''an University of Technology, Xi''an 710048, China;2. School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China;1. Control and Modelling Group (GCOM), Department of Electrical Engineering, Federal University of São João del-Rei – UFSJ, São João del-Rei, MG 36307-352, Brazil;2. Department of Mechatronics Engineering, Federal Center of Technological Education of Minas Gerais – CEFET-MG, Divinópolis, MG 35503-822, Brazil |
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| Abstract: | This paper addresses the distributed control of delayed interconnected nonlinear systems with time-varying delays in both the local subsystems’ dynamics and the physical interconnections among the subsystems. The Takagi–Sugeno fuzzy model with nonlinear consequent parts (N-TS), which is capable to provide less complex representations than standard T–S fuzzy models, is considered to efficiently deal with this class of complex systems. Then, based on Lyapunov–Krasovskii stability arguments, a synthesis condition is proposed to design a distributed control law such that the origin of the closed-loop interconnected system is locally asymptotically stable together with a guaranteed set of admissible initial conditions for which the validity of the N-TS fuzzy model is ensured. Moreover, a quasi-convex optimization procedure is formulated to enlarge the set of admissible initial conditions. The effectiveness of the proposed synthesis condition is validated in two numerical examples, including an interconnected power network with seven generators. |
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