Previous |  Up |  Next


event-triggered control; output feedback control; linear matrix inequality
This paper is concerned with the problem of $H_\infty$ event-triggered output feedback control of discrete time piecewise-affine systems. Relying on system outputs, a piecewise-affine triggering condition is constructed to release communication burden. Resorting to piecewise Lyapunov functional and robust control techniques, sufficient conditions are built to ensure the closed-loop systems to be asymptotically stable with the prescribed $H_\infty$ performance. By utilizing a separation strategy, the static output feedback controller is solved by means of linear matrix inequalities. The validity of the proposed method are demonstrated by numerical examples.
[1] Anders, R., Mikael, J.: Computation of piecewise quadratic Lyapunov functions for hybrid systems. IEEE Trans. Automat. Control (1998), 2005-2010. DOI 
[2] Antoine, G.: Dynamic triggering mechanisms for event-triggered control. IEEE Trans. Automat. Control 60 (2015), 1992-1997. DOI 
[3] Bengtsson, G., Lindahl, S.: A design scheme for incomplete state or output feedback with applications to boiler and power system control. Automatica 10 (1974), 15-30. DOI 
[4] Boyd, S., Ghaoui, L. E., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM 1994. Zbl 0816.93004
[5] Breschi, V., Piga, D., Bemporad, A.: iecewise affine regression via recursive multiple least squares and multicategory discrimination. Automatica 73 (2016), 155-162. DOI 
[6] Calise, A. J., Hovakimyan, N., Idan, M.: Adaptive output feedback control of nonlinear systems using neural networks. Automatica 37 (2001), 1201-1211. DOI 
[7] Chang, X., Yang, G.: New results on output feedback $ H_ {\infty} $ control for linear discrete-time systems. IEEE Trans. Automat. Control 59 (2014), 1355-1359. DOI 
[8] Chang, X., Zhang, L., Park, J. H.: Robust static output feedback $ H_ {\infty} $ control for uncertain fuzzy systems. Fuzzy Sets Systems 273 (2015), 87-104. DOI 
[9] Chao, D., Che, W., Shi, P.: Cooperative fault-tolerant output regulation for multiagent systems by distributed learning control approach. IEEE Trans. Neural Networks Learning Systems 31 (2019), 4831-4841. DOI 
[10] Chao, D., Che, W., Wu, Z.: A dynamic periodic event-triggered approach to consensus of heterogeneous linear multiagent systems with time-varying communication delays. IEEE Trans. Cybernet. xx (2020), 1812-1821. DOI 
[11] Eghbal, N., Pariz, N., Karimpour, A.: Discontinuous piecewise quadratic Lyapunov functions for planar piecewise affine systems. J. Math. Anal. Appl. 399 (2013), 586-593. DOI 
[12] Heemels, W., Donkers, M.: Model-based periodic event-triggered control for linear systems. Automatica 49 (2013), 698-711. DOI 
[13] Iervolino, R., Tangredi, D., Vasca, F.: Lyapunov stability for piecewise affine systems via cone-copositivity. Automatica 81 (2017), 22-29. DOI 
[14] Kantner, M.: Robust stability of piecewise linear discrete time systems. Proc. 1997 American Control Conference, IEEE 2 (1997), 1241-1245. DOI 
[15] Khashooei, A., Antunes, B., Heemels, W.: Output-based event-triggered control with performance guarantees. IEEE Trans. Automat. Control 62 (2017), 3646-3652. DOI 
[16] Liu, Y., Yang, G., Li, X.: Event-triggered fault detection observer design for affine fuzzy systems. Neurocomputing 267 (2017), 564-571. DOI 
[17] Ma, Y., Wu, W., Cui, B.: Event-triggered feedback control for discrete-time piecewise-affine systems. Int. J. Systems Sci. 49 (2018), 3377-3389. DOI 
[18] Ma, Y., Wu, W., Gorges, D., Cui, B.: Event-triggered feedback control for discrete-time piecewise affine systems subject to input saturation. Nonlinear Dynamics 95 (2018), 2353-2365. DOI 
[19] Mohammed, C., Guerra, T. M.: LMI solution for robust static output feedback control of discrete Takagi-Sugeno fuzzy models. IEEE Trans. Fuzzy Systems 20 (2012), 1160-1165. DOI 
[20] Palmieri, G., Baric, M., Glielmo, L., Borrelli, F.: Robust vehicle lateral stabilisation via set-based methods for uncertain piecewise affine systems. Vehicle System Dynamics 50 (2012), 861-882. DOI 
[21] Perez, J., Llopis, R. S.: Tuning and robustness analysis of event-based PID controllers under different event-generation strategies. Int. J. Control 91 (2018), 1567-1587. DOI 
[22] Ren, W., Yang, H., Jiang, B.: Fault recoverability analysis of nonlinear systems: A piecewise affine system approach. Int. J. Control Automat. Systems 15 (2017), 547-556. DOI 
[23] Shen, J., Lam, J.: Static output-feedback stabilization with optimal $L_1$-gain for positive linear systems. Automatica 63 (2016), 248-253. DOI 
[24] Song, X., Zhou, S., Zhang, B.: A cone complementarity linearization approach to robust $H_\infty$ controller design for continuous-time piecewise linear systems with linear fractional uncertainties. Nonlinear Analysis: Hybrid Systems 2 (2008), 1264-1274. DOI 
[25] Vaezi, M., Izadian, A.: Piecewise affine system identification of a hydraulic wind power transfer system. IEEE Trans. Control Systems Technol. 23 (2015), 2077-2086. DOI 
[26] Wang, X., Deng, Z., Ma, S., Du, X.: Event-triggered design for multi-agent optimal consensus of Euler-Lagrangian systems. Kybernetika 53 (2017), 179-194. DOI 
[27] Wei, Y., Qiu, J., Karimi, H. R.: A novel approach to sampled-data filter design for piecewise-affine systems. Automatica 109 (2019) 108481. DOI 
[28] Wei, Y., Qiu, J., Lam, H., Wu, L.: Approaches to T-S fuzzy-affine-model-based reliable output feedback control for nonlinear Ito stochastic systems. IEEE Trans. Fuzzy Systems 25 (2016), 569-583. DOI 
[29] Durrant-Whyte, H.: Autonomous land vehicles. J. Systems Control Engrg. 219 (2005), 77-94. DOI 
[30] Xie, L.: Output feedback $H_\infty$ control of systems with parameter uncertainty. Int. J. Control 63 (1996), 741-750. DOI 
[31] Yan, S., Zhang, G., Li, T., Shen, M., Li, L.: $H_\infty$ static output control of discrete-time networked control systems with an event-triggered scheme. Circuits 37 (2018), 553-568. DOI 
[32] Yang, R., Zheng, W., Yu, Y.: Event-triggered sliding mode control of discrete-time two-dimensional systems in Roesser model. Automatica 114 (2020), 108813. DOI 
[33] Zhang, H., and, Y. Shi, Mehr, A. S.: Robust static output feedback control and remote PID design for networked motor systems. IEEE Trans. Industr. Electronics 25 (2011), 5396-5405. DOI 
[34] Zhang, P., Wang, J.: Event-triggered observer-based tracking control for leader-follower multi-agent systems. Kybernetika 52 (2016), 589-606. DOI 
[35] Zhu, Y., Zhong, Z., Basin, M. V., Zhou, D.: A descriptor system approach to stability and stabilization of discrete-time switched PWA systems. IEEE Trans. Automat. Control 63 (2018), 3456-3463. DOI 
Partner of
EuDML logo