Analysis and synthesis of discrete nonlinear passive systems via affine TS fuzzy models

International Journal of Systems Science (Impact Factor: 2.1). 08/2008; 39(8):809-821. DOI: 10.1080/00207720801902580
Source: DBLP


The article considers the analysis and synthesis problem for the discrete nonlinear systems, which are represented by the discrete affine Takagi–Sugeno (T–S) fuzzy models. The state feedback fuzzy controller design methodology is developed to guarantee that the affine T–S fuzzy models achieve Lyapunov stability and strict input passivity. In order to find a suitable fuzzy controller, an Iterative Linear Matrix Inequality (ILMI) algorithm is employed in this article to solve the stability conditions for the closed-loop affine T–S fuzzy models. Finally, the application of the proposed fuzzy controller design methodology is manifested via a numerical example with computer simulations.

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Available from: Wei Chang
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    • "According to the discrete T-S fuzzy models, the stability analysis and synthesis have been considered in [5– 9]. Not only control schemes [5] [6] [7] [8] but also filter design methods [9] have been proposed for nonlinear discrete-time systems via T-S fuzzy model. In general, the stochastic signals and random parameters may exist in the real systems. "
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    ABSTRACT: This paper deals with the fuzzy controller design problem for discrete-time Takagi-Sugeno (T-S) fuzzy systems with multiplicative noises. Using the Lyapunov stability theory and Itô formula, the sufficient conditions are derived to guarantee the stability of the closed-loop nonlinear stochastic systems subject to actuator saturation. Based on the Parallel Distributed Compensation (PDC) concept, the fuzzy controller can be obtained to stabilize the T-S fuzzy models with multiplicative noises by combining the same membership functions of plants and desired state feedback gains. In order to illustrate the availability and practicability of proposed fuzzy controller design approach, the numerical simulations for the nonlinear truck-trailer system are given to demonstrate the applications of this paper.
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    • "Cao and Frank (2001), Guan and Chen (2004), Chen and Liu (2005), Lin, Wang, and Lee (2005), Lin, Wang, Lee, and He (2006), Hsiao (2007), Jun (2007), Zhang, Xu, Zang, and Zou (2007), Chu, Tsai, and Chang (2008) "
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    ABSTRACT: The problem of robust fuzzy control for a class of nonlinear fuzzy impulsive stochastic systems with time-varying delays is investigated. The nonlinear delay system is represented by the well-known T–S fuzzy model. The so-called parallel distributed compensation idea is employed to design the state feedback controller. Sufficient conditions for mean square exponential stability of the closed-loop system are derived in terms of linear matrix inequalities. Finally, a numerical example is given to illustrate the applicability of the theoretical results.
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    • "Generally, the strictly input passive type [8] [14] of passivity theory is utilized to achieve the attenuation performance. So, we also use the strictly input passive type for investigating the attenuation performance of system in this paper. "
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    ABSTRACT: The issue of observer-based robust passive fuzzy controller design is discussed and investigated in this paper for uncertain stochastic Takagi-Sugeno (T-S) fuzzy model with external disturbance. For describing the stochastic behaviors of system, the stochastic differential equation is used to structure the stochastic T-S fuzzy model for representing the nonlinear stochastic systems. Using the Lyapunov function and passivity theory, the sufficient stability condition can be derived in term of linear matrix inequality (LMI) by Ito¿'s formula. With stability conditions, a less conservatism design method is developed to synthesize the state feedback fuzzy controller and fuzzy observer for guaranteeing the asymptotical stability and strictly input passivity of system in the mean square.
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