Abstract
This paper focuses on the robust sensor fault-tolerant control of T–S fuzzy descriptor systems with unmeasurable premise variables subject to external disturbances. By introducing sensor fault as an auxiliary state vector, an augmented fuzzy descriptor system is constructed. A robust fuzzy descriptor observer is investigated to achieve simultaneous reconstruction of system states and sensor faults using descriptor approach and the \(L_2\) techniques to minimize the effect of the perturbations on the state estimation error. Based on the state estimated variables and by isolating the sensor fault, a fault-tolerant control scheme is proposed using a state feedback controller approach such that the resulting closed-loop system is stable with prescribed \(H_{\infty }\) performance. Sufficient conditions for the existence of a robust fuzzy descriptor observer and a fault-tolerant controller are derived in the sense of Lyapunov asymptotic stability and are formulated in terms of a series of linear matrix inequalities without additional constraints. Finally, a numerical example was discussed to prove the performance of the proposed approach.
Similar content being viewed by others
References
Dai, L.: Singular Control Systems. Springer, New York (1989)
Duan, G.R.: Analysis and Design of Descriptor Linear Systems. Springer, New York (2010)
Mills, J.K., Goldenberg, A.: Force and position control of manipulators during contrained motion tasks. IEEE Trans. Robot. Autom. 5, 30–46 (1989)
Luenberger, D.: Dynamic equation in descriptor form. IEEE Trans. Autom. Control 22, 312–321 (1977)
Taniguchi T., Tanaka K., Yamafuji K., Wang H. Fizzy descriptor systems: stability analysis and design via lmis. In: Proceedings of the American Control Conference, pp. 1827–1831, San Diego, (1999)
Wang, Y., Sun, Z.Q., Sun, F.C.: Robust fuzzy control of a class of nonlinear descriptor systems with time-varying delay. Int. J. Control Autom. Syst. 2, 76–82 (2004)
Taniguchi, T., Tanaka, K., Wang, H.O.: Fuzzy descriptor systems and nonlinear model following control. IEEE Trans. Fuzzy Syst. 8, 442–452 (2000)
Han, C., Zhang, G., Wu, L., Zeng, Q.: Sliding mode control of T–S fuzzy descriptor systems with time-delay. J. Frankl. Inst. 349, 1430–1444 (2012)
Yuan, Y., Zhang, Q., Zhang, D., Chen, B.: Admissible conditions of fuzzy descriptor systems based on fuzzy lyapunov function approach. Int. J. Inf. Syst. Sci. 4, 219–232 (2008)
Tanaka, K., Wang, H.O.: uzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. Wiley, Hoboken (2001)
Chaabane, M., Tadeo, T., Mehdi, D., Souissi, M.: On the robust admissibilization of descriptor systems by static output-feedback: an LMI approach. Math. Prob. Eng. 1–9, 2011 (2011)
Chaabane, M., Bachelier, O., Souissi, M., Mehdi, D.: Stability and stabilizability of continuous descriptor systems: an LMI approach. Math. Prob. Eng. 1–15, 2006 (2006)
Gassara, H., Kchaou, M., El Hajjaji, A., Chaabane, M.: Control of time delay fuzzy descriptor systems with actuator saturation. Circuits Syst. Signal Process 34, 3739–3756 (2014)
Guerra, T.M., Estrada-Manzo, V., Lendek, Z.: Observer design for Takagi-Sugeno descriptor models: an LMI approach. Automatica 52, 154–159 (2015)
Fan, H., Meng, M., Fen, J.: Observers of fuzzy descriptor systems with time-delays. Abstr. Appl. Anal. 1–9, 2014 (2014)
Essabre, M.: Fuzzy observer design for a class of Takagi-Sugeno descriptor systems. Contemp. Eng. Sci. 7, 149–164 (2014)
Liu, P., Yang, W.T., Yang, C.E.: Robust observer-based output feedback control for fuzzy descriptor systems. Expert Syst. Appl. 40, 4503–4510 (2013)
Hamdi H., Rodrigues M., Mechmech C., HadjBraiek N.B.: Robust \(H_{\infty }\) fault diagnosis for multi-model descriptor systems: a multi-objective approach. In 18th mediterranean conference on control automation MED’10, pp. 833–838, Marrakech 23–25 July 2010
Hamdi, H., Rodrigues, M., Mechmeche, C., Theilliol, D., Benhadj, N.B.: Fault detection and isolation in linear parameter-varying descriptor systems via proportional integral observer. Int. J. Adapt. Control Signal Process. 26, 224–240 (2012)
Zhu B., Zhang D., Zhang Q., Xing S.. Dissipative fault-tolerant control for T–S fuzzy descriptor systems. In Proceedings of the 32nd chinese control conference, Xi’an, 26–28 July 2013
Jia, Q., Chen, W., Zhang, Y., Li, H.: Fault reconstruction and fault-tolerant control via learning observers in TakagiSugeno fuzzy descriptor systems with time delays. IEEE Trans. Ind. Electro. 62, 3885–3895 (2015)
Gao, Z., Shi, X., Ding, S.X.: Fuzzy state disturbance observer design for T–S fuzzy systems with application to sensor fault estimation. IEEE Trans. SMC Part B Cybern. 38, 875–880 (2008)
Bouattour, M., Chadli, M., Chaabane, M., El Hajjaji, A.: Design of robust fault detection observer for Takagi-Sugeno models using the descriptor approach. Int. J. Control Autom. Syst. 9, 973–979 (2011)
Chadli, M., EL Hajjaji, A.: Comment on observer-based robust fuzzy control of nonlinear systems with parametric uncertainties. Fuzzy Sets Syst. 157, 1276–1281 (2006)
GueltonK.: Estimation des caractTristiques du mouvement humain en station debout. Mise en oeuvre dobservateurs flous sous forme descripteur UniversitT de Valenciennes et du Hainaut-CambrTsis. PhD thesis, UniversitT de Valenciennes et du Hainaut-CambrTsis, 2003
Marx, B., Ragot, J.: Stability and \(L_2\) norm bound conditions for takagi-sugeno descriptor systems. In World congress the international federation of automatic control (IFAC), Seoul (2008)
Kuo C.H., Fang C.H.: An LMI approach to admissibilization of unceratin descriptor systems via static output feedback. In American control conference, pp. 5104–5109, Denver, 4–6 June 2003
Lin, C., Wang, Z., Yang, F.: Observer-based networked control for continuous-time systems with random sensor delays. Automatica 45, 578–584 (2009)
Qiu, J., Wei, Y., Karimi, H.R.: New approach to delay-dependent \(H_{\infty }\) control for continuous-time Markovian jump systems with time-varying delay and deficient transition descriptions. J. Franklin Inst. 352, 189–215 (2015)
Wu, Z., Su, H., Chu, J.: \(H_{\infty }\) filtering for singular Markovian jump systems with time delay. Int. J. Robust Nonlinear Control 20, 939–957 (2010)
Zhou, S., Li, T.: Robust stabilization for delayed discrete-time fuzzy systems via basisdependent Lyapunov-Krasovskii function. Fuzzy Sets Syst. 151, 139–153 (2005)
Choi, D.J., Park, P.G.: \(H_{\infty }\) state-feedback controller design for discrete-time fuzzy systems using fuzzy weighting-dependent Lyapunov functions. IEEE Trans. Fuzzy Syst. 11, 271–278 (2003)
Johansson, M., Rantzer, A., Arzen, K.E.: Piecewise quadratic stability of fuzzy systems. IEEE Trans. Fuzzy Syst. 7, 713–722 (1999)
Qiu, J., Tian, H., Lu, Q., Gao, H.: Nonsynchronized robust filtering design for continuous-time TS fuzzy affine dynamic systems based on piecewise Lyapunov functions. IEEE Trans. Cybern. 43, 1755–1766 (2013)
Qiu, J., Feng, G., Gao, H.: Static-output-feedback \(H_{\infty }\) control of continuous-time TS fuzzy affine systems via piecewise Lyapunov functions. IEEE Trans. Fuzzy Syst. 21, 245–261 (2013)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Haj Brahim, I., Chaabane, M. & Mehdi, D. Fault-Tolerant Control for T–S Fuzzy Descriptor Systems with Sensor Faults: An LMI Approach. Int. J. Fuzzy Syst. 19, 516–527 (2017). https://doi.org/10.1007/s40815-016-0154-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40815-016-0154-4