IFAC PapersOnLine 50-1 (2017) 2989–2994 ScienceDirect ScienceDirect Available online at www.sciencedirect.com 2405-8963 © 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2017.08.665 © 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Stability Analysis of Nonlinear Networked Control Systems via Takagi-Sugeno Fuzzy Model Jun Yoneyama * * Aoyama Gakuin University, Sagamihara, Kanagawa, 252-5258 Japan (e-mail: yoneyama@ee.aoyama.ac.jp). Abstract: The paper is concerned with stability analysis of nonlinear networked systems which are described by the Takagi-Sugeno fuzzy systems. In the networked control system, the information is exchanged with packets through a network where the data packets encounter delays. The closed-loop system with a controller can be modeled as a fuzzy system with time- varying delays in sensor and actuator modes. Based on a novel Lyapunov-Krasovskii stability theorem, the stability analysis problem of a fuzzy system with time-varying delays is considered. Multiple Lyapunov-Krasovskii function with multiple integral functions allows us to obtain less conservative conditions for the networked control system to be asymptotically stable. In fact, this method drastically reduces the conservatism in stability conditions. Keywords: Fuzzy systems, Intelligent control, Networks, Nonlinear control systems, Time-delay. 1. INTRODUCTION Most physical systems are nonlinear and they appear in many engineering fields. In the past three decades, Takagi- Sugeno fuzzy model has been widely used for nonlinear control systems since it can universally approximate or can exactly describe general nonlinear systems(Lam et al. (2000), Takagi and Sugeno (1985), and Tanaka and Sugeno (1992)). In fact, Takagi-Sugeno fuzzy model has played an important role for nonlinear system analysis and its control design. The stability of fuzzy systems was investigated in Lee et al. (2014), Tanaka and Sugeno (1992), Teixiera et al. (2003), and Tuan et al. (2001). The recent paper by Lee et al. (2014) gave novel stability conditions but no control design method was provided there. Fuzzy control theory has been extended to a class of fuzzy systems with local nonlinear systems in Yoneyama (2014). Yoneyama (2014) greatly reduces conservatism in control design conditions. Such a generalized fuzzy system has been considered, and stability and stabilizability conditions have been obtained. However, those conditions are still conservative, and there is room to improve. Many results on the state feedback controller design method have appeared in the literature(for example, Lam et al. (2000), Precup et al. (2012), Tanaka and Sugeno (1992), Wang et al. (1996), and references therein.). The paper by Lam et al. (2000) uses a state feedback parallel distributed compansator(PDC), whose membership func- tions are mismatched with local controlled systems, and gives less conservative stability conditions than those of Tanaka and Sugeno (1992) and Wang et al. (1996). The paper by Precup et al. (2012) recently provided a state feedback control method by iterative technique but still needs much computational load. The paper by Tanaka et al. (2007) adopted a descriptor system approach, which re- duces control design conditions for the state feedback con- trol design. The paper by Guelton et al. (2009) extended the descriptor system approach to the case of the output feedback control design. It is well-known that although descriptor systems are more complicated than state-space systems, they have richer structures, which produces less conservatism in the control design conditions. Those two papers used a multiple Lyapunov matrix method, which is a generalization of a common Lyapunov matrix method. The papers by Li et al. (2016), Marouf et al. (2016), and Zhang et al. (2007) considered control design problems for nonlinear networked control systems. Li et al. (2016) partially introduced a multiple Lyapunov-Krasovskii ma- trix method for fuzzy systems with time-delay but it is not a general multiple matrix method. Marouf et al. (2016) employed a common Lyapunov-Krasovskii function method with descriptor system approach, which is still more conservative than a multiple Lyapunov-Krasovskii matrix method. In this paper, we consider a nonlinear networked control system design based on Takagi-Sugeno fuzzy models. First, we assume a special form of fuzzy feedback controller and consider the closed-loop system with such a feedback controller. In order to obtain less conservative stability conditions, we introduce a new type of multiple Lyapunov- Krasovskii function, which reduces the conservatism in our stability condition. Such a new multiple Lyapunov- Krasovskii function employs an integral of the member- ship functions of fuzzy systems. A multiple Lyapunov- Krasovskii function is a natural extension of a common Lyapunov function. However, since a conventional multiple Lyapunov-Krasovskii function contains the membership function, a resulting stability condition depends on the derivatives of the membership function that is a function of the premise variables. However, the membership function