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This study presents a linear matrix inequality (LMI) approach to the sampled-data control of Takagi–Sugeno fuzzy systems, based on the intelligent digital redesign (IDR) technique. The objective of the IDR is to design a digital control system whose trajectory closely matches that of a given well-constructed analogue control system by minimising the state-matching error. In this study, state-matching performance is enhanced by using a continuous-time state-matching criterion, which guarantees that the state-matching error is minimised through the entire time interval. Unlike previous studies, mismatched information of membership functions for both analogue and digital control systems is directly manipulated. Moreover, the authors introduce an improved fuzzy Lyapunov functional that consists of both membership functions for analogue and digital control systems, which relaxes the conservativeness of LMI conditions. Finally, two examples demonstrating the effectiveness of the authors' method are provided.
In this study, a novel intelligent digital redesign (IDR) technique is proposed for the sampled-data fuzzy controller of the non-linear system with packet losses. For the IDR development, the non-linear system is represented in the Takagi–Sugeno fuzzy model and the packet loss is assumed to be an independent, identically distributed Bernoulli random process. After introducing the traditional IDR technique, the closed-loop system with state-matching error and the state-matching error cost function are achieved for the development of the novel IDR technique. In the discrete-time Lyapunov sense, the exponential mean-square stability is guaranteed while minimising the state-matching error, and its sufficient condition is derived into linear matrix inequalities. Two examples are provided to verify the effectiveness of the proposed technique by comparison.
A novel linear matrix inequality (LMI) condition for the stability of the sampled-data fuzzy control system based on the Takagi-Sugeno fuzzy model is presented. Using the novel Lyapunov functional, the relaxed stability condition is presented for the sampled-data fuzzy control and represented in the LMI format. A simulation example is provided to verify the effectiveness of the proposed technique.
This study proposes an intelligent digital redesign (IDR) technique for sampled-data fuzzy filters of non-linear systems. The technique constructs a closed-loop system with predesigned continuous-time and sampled-data filters based on the Takagi–Sugeno (T–S) fuzzy model. The closed-loop systems ensure asymptotic stability and state-matching condition in the IDR problem. Unlike previous techniques, the proposed method solves the IDR problem without a discretization process which degrades the IDR performance. Sufficient conditions for solving the IDR problem are proposed and derived in terms of linear matrix inequalities. In addition, the performance recovery of the sampled-data fuzzy filter is shown. Finally, the feasibility of the proposed technique is demonstrated in two simulation examples.