Abstract
This chapter presents a static output feedback controller design method for nonlinear systems represented by Takagi-Sugeno (T–S) fuzzy models. A new quadratic stabilization result based on Parallel Distributed Compensation (PDC) structure is developed to design a static output PDC (OPDC) controller. Based on the well known existing method in the literature, two methods are proposed. The design of the controller by static output feedback is given by two different sets of LMIs. Two examples are presented to illustrate these results.
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References
Elghaoui L, Oustry F, Aitrami M (1997) A cone complementary linearization algorithm for static output-feedback and related problems. IEEE Trans Aut Control 42:1171–1176
Chadli M, Maquin D, Ragot J (2002) An LMI formulation for output feedback stabilization in multiple model approach. In: 41th Conference decision control. Las Vegas, 10–13 Dec 2002, pp 311–316
Wang HO, Tanaka K, Griffin MF (1996) An approach to fuzzy control of nonlinear systems: stability and design issues. IEEE Trans Fuzzy Syst 4:14–23
Daafouz J, Riedinger P, Iung C (2002) Stability analysis and control synthesis for switched systems: a switched Lyapunov function spproach. IEEE Trans Aut Control 47:1883–11887
Feng G (2004) Stability analysis of discrete-time fuzzy dynamic systems based on piecewise Lyapunov functions. IEEE Trans Fuzzy Syst 12:22–28
Johansson M, Rantzer A, Arzen KE (1999) Piecewise quadratic stability of fuzzy systems. IEEE Trans Fuzzy Syst 7:713–722
Shorten R, Narenda KS, Mason O (2003) A result on common quadratic Lyapunov functions. IEEE Trans Aut Control 48:110–113
Benzaouia A, Mehdi D, El Hajjaji A. Nachidi M (2007) Piecewise quadratic Lyapunov function for nonlinear systems with fuzzy static output feedback control. In: European control conference. Kos, Greece, 2–5 July 2007
Nachidi M, Tadeo F, Hmamed A, Benzaouia A (2007) Static output-feedback stabilization for time-delay Takagi-Sugeno fuzzy systems. In: \(46^{th}\) Conference decision control. New Orleans, 12–14 Dec 2007, pp 1634–1639
Nachidi M, Benzaouia A, Tadeo F, Ait Rami M (2008) LMI-based approach for output feedback stabilization for discrete-time Takagi-Sugeno systems. IEEE Trans Fuzzy Syst 16:1188–1196
De Olivera MC, Skelton RE (2001) Stability tests for constrained linear systems, perspective in robust control. Springer, LNCIS
Tanaka K, Sano M (1994) A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer. IEEE Trans Fuzzy Syst 2:119–134
Yoneyama Y, Nishikawa M, Katayama H, Ichikawa A (2000) Output stabilization of Takagi-Sgugeno fuzzy systems. Fuzzy Sets Syst 111:253–266
Benzaouia A (2012) Saturated switching systems. Springer, SLNC
Nachidi M (2009) Stabilization of Takagi-Sugeno fuzzy systems with application on a greenhouse (Ph. D. thesis). University of Valladolid, Spain
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Benzaouia, A., El Hajjaji, A. (2014). Static Output Feedback Control for Fuzzy Systems. In: Advanced Takagi‒Sugeno Fuzzy Systems. Studies in Systems, Decision and Control, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-05639-5_3
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DOI: https://doi.org/10.1007/978-3-319-05639-5_3
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