An Lmi-based Approach To Static Output Feedback Stabilization Of T-s Fuzzy Systems

The problem of static output feedback control design for continuous-time Takagi- Sugeno (T-S) fuzzy systems is addressed in this paper. The membership functions are modeled in a space defined by the Cartesian product of simplexes, called multi-simplex, and are allowed to vary arbitrarily (i.e. no bounds on the time-derivative of the membership functions are assumed). The static output feedback fuzzy controller is obtained through a two-step procedure: first, a stabilizing fuzzy state feedback control gain is determined by means of linear matrix inequalities (LMIs). Then, the state feedback gain matrices are used in LMI conditions that, if satisfied, provide the fuzzy static output feedback control law. A fuzzy line integral Lyapunov function with arbitrary polynomial dependence on the premise variables is used to assess closedloop stability. The main appeal of the approach is that the output feedback gains can have independent and arbitrary polynomial dependence on some specific premise variables, selected by the designer, with great advantages for practical applications. An example illustrates that the proposed strategy can provide less conservative results when compared to other methods from the literature for output feedback stabilization of continuous-time T-S fuzzy systems. © 2011 IFAC.18PART 11259312598Agulhari, C.M., Oliveira, R.C.L.F., Peres, P.L.D., Robust H ∞ static output-feedback design for time-invariant discrete-time polytopic systems from parameter-dependent state-feedback gains (2010) Proceedings of the 2010 American Control Conference, pp. 4677-4682. , Baltimore, MD, USA, June-JulyArzelier, D., Peaucelle, D., An iterative method for mixed H 2/H ∞ synthesis via static output-feedback (2002) Proceedings of the 41st IEEE Conference on Decision and Control, pp. 3464-3469. , Las Vegas, NV, USA, DecemberArzelier, D., Peaucelle, D., Salhi, S., Robust static output feedback stabilization for polytopic uncertain systems: Improving the guaranteed performance bound (2003) Proceedings of the 4th IFAC Symposium on Robust Control Design (ROCOND 2003), , Milan, Italy, JuneArzelier, D., Gryazina, E.N., Peaucelle, D., Polyak, B.T., Mixed LMI/Randomized methods for static output feedback control design (2010) Proceedings of the 2010 American Control Conference, pp. 4683-4688. , Baltimore, MD, USA, June-JulyBaranyi, P., TP model transformation as a way to LMIbased controller design (2004) IEEE Transactions on Industrial Electronics, 51 (2), pp. 387-400. , AprilBouarar, T., Guelton, K., Manamanni, N., Static output feedback controller design for Takagi-Sugeno systems - A fuzzy Lyapunov LMI approach (2009) Proceedings of the 48th IEEE Conference on Decision and Control - 28th Chinese Control Conference, pp. 4150-4155. , Shanghai, P. R. China, DecemberFang, C.-H., Liu, Y.-S., Kau, S.-W., Hong, L., Lee, C.-H., A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems (2006) IEEE Transactions on Fuzzy Systems, 14 (3), pp. 386-397. , JuneGuelton, K., Bouarar, T., Manamanni, N., Robust dynamic output feedback fuzzy Lyapunov stabilization of Takagi-Sugeno systems - A descriptor redundancy approach (2009) Fuzzy Sets and Systems, 160 (19), pp. 2796-2811. , OctoberGuerra, T.M., Kruszewski, A., Vermeiren, L., Tirmant, H., Conditions of output stabilization for nonlinear models in the Takagi-Sugeno's form (2006) Fuzzy Sets and Systems, 157 (17), pp. 1248-1259. , MayHuang, D., Nguang, S.K., Static output feedback controller design for fuzzy systems: An ILMI approach (2007) Information Sciences, 177 (14), pp. 3005-3015. , JulyLee, H.J., Kim, D.W., Fuzzy static output feedback may be possible in LMI framework (2009) IEEE Transactions on Fuzzy Systems, 17 (5), pp. 1229-1230. , OctoberMansouri, B., Manamanni, N., Guelton, K., Kruszewski, A., Guerra, T.M., Output feedback LMI tracking control conditions with H ∞ criterion for uncertain and disturbed T-S models (2009) Information Sciences, 179 (4), pp. 446-457. , FebruaryMehdi, D., Boukas, E.K., Bachelier, O., Static output feedback design for uncertain linear discrete time systems (2004) IMA Journal of Mathematical Control and Information, 21 (1), pp. 1-13. , MarchMozelli, L.A., Palhares, R.M., Avellar, G.S.C., A systematic approach to improve multiple Lyapunov function stability and stabilization conditions for fuzzy systems (2009) Information Sciences, 179 (8), pp. 1149-1162. , MarchMozelli, L.A., Palhares, R.M., Souza, F.O., Mendes, E.M.A.M., Reducing conservativeness in recent stability conditions of TS fuzzy systems (2009) Automatica, 45 (6), pp. 1580-1583. , JuneNguang, S.K., Shi, P., Robust H ∞ output feedback control design for fuzzy dynamic systems with quadratic D stability constraints: An LMI approach (2006) Information Sciences, 176 (15), pp. 2161-2191. , AugustPeaucelle, D., Arzelier, D., An efficient numerical solution for H 2 static output feedback synthesis (2001) Proceedings of the 2001 European Control Conference, , Porto, Portugal, SeptemberRhee, B.-J., Won, S., A new fuzzy Lyapunov function approach for a Takagi-Sugeno fuzzy control system design (2006) Fuzzy Sets and Systems, 157 (9), pp. 1211-1228. , MaySyrmos, V.L., Abdallah, C.T., Dorato, P., Grigoriadis, K., Static output feedback - A survey (1997) Automatica, 33 (2), pp. 125-137. , FebruaryTakagi, T., Sugeno, M., Fuzzy identification of systems and its applications to modeling and control (1985) IEEE Transactions on Systems, Man, and Cybernetics, SMC-15 (1), pp. 116-132. , JanuaryTanaka, K., Hori, T., Wang, H.O., A fuzzy Lyapunov approach to fuzzy control system design (2001) Proceedings of the 2001 American Control Conference, pp. 4790-4795. , Arlington, VA, USA, JuneTanaka, K., Hori, T., Wang, H.O., A multiple Lyapunov function approach to stabilization of fuzzy control systems (2003) IEEE Transactions on Fuzzy Systems, 11 (4), pp. 582-589. , AugustTognetti, E.S., Oliveira, R.C.L.F., Peres, P.L.D., Selective stabilization of Takagi-Sugeno fuzzy systems (2010) Proceedings of the 2010 IEEE International Conference on Fuzzy Systems, pp. 2772-2779. , Barcelona, Spain, Jul