Lin, H.; Antsaklis, P. J. Hybrid state feedback stabilization with \(l_{2}\) performance for discrete-time switched linear systems. (English) Zbl 1152.93472 Int. J. Control 81, No. 7, 1114-1124 (2008). Summary: In this paper, the co-design of continuous-variable controllers and discrete-event switching logics, both in state feedback form, is investigated for a class of discrete-time switched linear control systems. It is assumed that none of the subsystems is stabilized through a continuous state feedback alone. However, it is possible to stabilize the whole switched system via carefully designing both the continuous controllers and the switching logics. Sufficient synthesis conditions for this co-design problem are proposed here in the form of bilinear matrix inequalities, which is based on the argument of multiple Lyapunov functions. The closed-loop switched system forms a special class of linear hybrid system, and is shown to be asymptotically stable with a finite \(l_{2}\) induced gain. Cited in 20 Documents MSC: 93D15 Stabilization of systems by feedback 93C55 Discrete-time control/observation systems PDFBibTeX XMLCite \textit{H. Lin} and \textit{P. J. Antsaklis}, Int. J. Control 81, No. 7, 1114--1124 (2008; Zbl 1152.93472) Full Text: DOI References: [1] DOI: 10.1016/S0005-1098(98)00178-2 · Zbl 1049.93514 · doi:10.1016/S0005-1098(98)00178-2 [2] Borrelli F, Constrained Optimal Control of Linear and Hybrid Systems, LNCIS 290 (2003) · Zbl 1030.49036 [3] Boyd S, Linear Matrix Inequalities in System and Control Theory (1994) [4] DOI: 10.1109/9.664150 · Zbl 0904.93036 · doi:10.1109/9.664150 [5] DOI: 10.1109/TAC.2005.846594 · Zbl 1365.93389 · doi:10.1109/TAC.2005.846594 [6] Corona, D, Giua, A and Seatzu, C. 2005. Stabilization of switched systems via optimal control. Proceedings of the 16th IFAC World Congress. 2005, Prague, Czech Republic. · Zbl 1071.93028 [7] DOI: 10.1109/TAC.2002.804474 · Zbl 1364.93559 · doi:10.1109/TAC.2002.804474 [8] Decarlo RA, Proceedings of the IEEE: Special Issue on Hybrid Systems 88 pp 1069– (2000) [9] DOI: 10.1016/j.sysconle.2005.04.005 · Zbl 1129.93497 · doi:10.1016/j.sysconle.2005.04.005 [10] Fang, L, Lin, H and Antsaklis, PJ. 2004. Stabilization and performance analysis for a class of switched systems. Proceedings of the 43rd IEEE Conf. Decision Control. 2004, Paradise Island, Bahamas. pp.3265–3270. [11] Feron E, ”Quadratic stabilizability of switched systems via state and output feedback” (1996) [12] Hassibi, A, Boyd, SP and How, JP. 1999. Control of asynchronous dynamical systems with rate constraints on events. Proceedings of the 38th IEEE Conf. Decision Control. 1999, Phoenix, AZ. pp.1345–1351. [13] DOI: 10.1109/TAC.2003.819300 · Zbl 1364.93213 · doi:10.1109/TAC.2003.819300 [14] DOI: 10.1109/TAC.2005.849187 · Zbl 1365.93400 · doi:10.1109/TAC.2005.849187 [15] DOI: 10.1007/978-1-4612-0017-8 · doi:10.1007/978-1-4612-0017-8 [16] DOI: 10.1109/37.793443 · Zbl 1384.93064 · doi:10.1109/37.793443 [17] Lin, H and Antsaklis, PJ. 2005. Stability and stabilizability of switched linear systems: a short survey of recent results. Proceedings of the 2005 ISIC-MED Joint Conference. 2005, Limassol, Cyprus. pp.24–29. [18] Lin, H and Antsaklis, PJ. 2006. Switching stabilization andl2gain performance controller synthesis for discrete-time switched linear systems. Proceedings of the 45th IEEE Conf. Decision Control. 2006, San Diego, CA. pp.2673–2678. [19] DOI: 10.1109/TAC.2007.894515 · Zbl 1366.93580 · doi:10.1109/TAC.2007.894515 [20] DOI: 10.1109/81.739260 · Zbl 0981.93055 · doi:10.1109/81.739260 [21] Mignone, D, Ferrari-Trecate, G and Morari, M. 2000. Stability and stabilization of piecewise affine and hybrid systems: an LMI approach. Proceedings of the 39th IEEE Conf. Decision Control. 2000, Sydney, Australia. pp.504–509. [22] Pettersson, S. 2003. Synthesis of switched linear systems. Proceedings of the 42nd IEEE Conf. Decision Control. 2003, Hawaii. pp.5283–5288. [23] Pettersson S, Proceedings of the 2004 American Control Conf pp 3869– (2004) [24] Pettersson S, Proceedings of the 2001 American Contr. Conf. pp 223– (2001) [25] DOI: 10.1016/j.sysconle.2005.01.002 · Zbl 1129.93401 · doi:10.1016/j.sysconle.2005.01.002 [26] DOI: 10.1016/S0005-1098(98)00167-8 · Zbl 0949.93014 · doi:10.1016/S0005-1098(98)00167-8 [27] DOI: 10.1016/j.automatica.2005.06.014 · Zbl 1100.93523 · doi:10.1016/j.automatica.2005.06.014 [28] Sun Z, Switched Linear Systems: Control and Design (2005) · doi:10.1007/1-84628-131-8 [29] Wicks MA, Proceedings of the 1997 American Contr. Conf pp 1709– (1997) [30] Wicks MA, Euro. J. Control 4 pp 140– (1998) · Zbl 0910.93062 · doi:10.1016/S0947-3580(98)70108-6 [31] DOI: 10.1016/S0016-0032(01)00030-8 · Zbl 1022.93017 · doi:10.1016/S0016-0032(01)00030-8 [32] DOI: 10.1080/0020717031000114968 · Zbl 1034.93055 · doi:10.1080/0020717031000114968 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.