×
Wu, Jenq-Lang

Singular \(L_2\)-gain control for switched nonlinear control systems under arbitrary switching. (English) Zbl 1466.93062

Int. J. Robust Nonlinear Control 30, No. 10, 4149-4163 (2020).
Summary: This article concerns with the synthesis of \(L_2\)-gain state feedback controllers, without the standard regular assumption, for multi-input switched nonlinear control-affine systems under arbitrary switching. A common control storage function approach is developed for deriving sufficient conditions for the existence of uniform \(L_2\)-gain controllers. Moreover, an explicit formula for constructing \(L_2\)-gain controllers is presented. A numerical example is given for illustration.

Cited in 2 Documents

MSC:

93B52 Feedback control
93D30 Lyapunov and storage functions
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93C10 Nonlinear systems in control theory

Keywords:

arbitrary switching; \(L_2\)-gain control; nonlinear control systems; state feedback; storage function; switched control systems
Cite Review PDF
Full Text: DOI

References:

[1] LiberzonD. Switching in Systems and Control. Boston: Birkhauser; 2003. · Zbl 1036.93001
[2] BrockettRW. Asymptotic stability and feedback stabilization. Differential Geometric Control Theory. Boston: Birkhauser; 1983:181‐191. · Zbl 0528.93051
[3] AgrachevAA, LiberzonD. Lie‐algebraic stability criteria for switched systems. SIAM J Control Optim. 2001;40:253‐269. · Zbl 0995.93064
[4] ColaneriP, GeromelJC, AstolfiA. Stabilization of continuous‐time switched nonlinear systems. Syst Control Lett. 2008;57:95‐103. · Zbl 1129.93042
[5] El‐FarraNH, MhaskarP, ChristofidesPD. Output feedback control of switched nonlinear systems using multiple Lyapunov functions. Syst Control Lett. 2005;54:1163‐1182. · Zbl 1129.93497
[6] LiberzonD, MorseAS. Basic problems in stability and design of switched systems. IEEE Control Syst Mag. 1999;19:59‐70. · Zbl 1384.93064
[7] LongL, ZhaoJ. Adaptive disturbance rejection for strict‐feedback switched nonlinear systems using multiple Lyapunov functions. Int J Robust Nonlinear Control. 2014;24(13):1887‐1902. · Zbl 1301.93092
[8] MaR, ZhaoJ. Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings. Automatica. 2010;46(11):1819‐1823. · Zbl 1218.93075
[9] MaR, ZhaoJ, DimirovskiGM. Backstepping design for global robust stabilisation of switched nonlinear systems in lower triangular form. Int J Syst Sci. 2013;44(3):615‐624. · Zbl 1276.93068
[10] MaR, DimirovskiGM, ZhaoJ. Backstepping robust H_∞ control for a class of uncertain switched nonlinear systems under arbitrary switchings. Asian J Control. 2013;15(1):41‐50. · Zbl 1327.93155
[11] VuL. Common Lyapunov functions for families of commuting nonlinear systems. Syst Control Lett. 2005;54:405‐416. · Zbl 1129.34321
[12] WangM, ZhaoJ, DimirovskiGM. H_∞ control for a class of cascade switched nonlinear systems. Asian J Control. 2008;10(6):724‐729.
[13] WuJL. Feedback stabilization for multi‐input switched nonlinear systems: two subsystems case. IEEE Trans Autom Control. 2008;53:1037‐1042. · Zbl 1367.93545
[14] WuJL. Stabilizing controllers design for switched nonlinear systems in strict‐feedback form. Automatica. 2009;45(4):1092‐1096. · Zbl 1162.93030
[15] ZhaoJ, DimirovskiGM. Quadratic stability of a class of switched nonlinear systems. IEEE Trans Autom Control. 2004;49:574‐578. · Zbl 1365.93382
[16] LiZ, ZhaoJ. Co‐design of controllers and a switching policy for nonstrict feedback switched nonlinear systems including first‐order feedforward paths. IEEE Trans Autom Control. 2018;64(4):1753‐1760. · Zbl 1482.93288
[17] LouZE, ZhaoJ. Immersion‐and invariance‐based adaptive stabilization of switched nonlinear systems. Int J Robust Nonlinear Control. 2018;28(1):197‐212. · Zbl 1387.93134
[18] XieJ, YangD, ZhaoJ. Switched adaptive control for a class of switched nontriangular nonlinear systems with vanishing control gains. Int J Robust Nonlinear Control. 2019;29(9):2603‐2618. · Zbl 1418.93134
[19] SunY, ZhaoJ. Finite‐time H_∞ control for switched nonlinear systems. Int J Control. Taylor (Accessed 24 May 2019). https://doi.org/10.1080/00207179.2019.1617899. · Zbl 1485.93524 · doi:10.1080/00207179.2019.1617899
[20] YinY, ZhaoX, ZhengX. New stability and stabilization conditions of switched systems with mode‐dependent average dwell time. Circuits Syst Signal Process. 2017;36(1):82‐98. · Zbl 1368.93581
[21] MaL, HuoX, ZhaoX, ZongG. Adaptive fuzzy tracking control for a class of uncertain switched nonlinear systems with multiple constraints: a small‐gain approach. Int J Fuzzy Syst. 2019;21(8):2609‐2624.
[22] ZhaoX, WangX, MaL, ZongG. Fuzzy‐approximation‐based asymptotic tracking control for a class of uncertain switched nonlinear systems. IEEE Trans Fuzzy Systems. 2020;28:632‐644.
[23] ArtsteinZ. Stabilization with relaxed control. Nonlinear Anal Theory Methods Appl. 1983;7:1163‐1173. · Zbl 0525.93053
[24] KokotovicPP, ArcakM. Constructive nonlinear control: a historical perspective. Automatica. 2001;37:637‐662. · Zbl 1153.93301
[25] KrsticM, KanellakopoulosI, KokotovicP. Nonlinear and Adaptive Control Design. New York, NY: Wiley‐Interscience; 1995.
[26] SontagED. A Lyapunov‐like characterization of asymptotic controllability. SIAM J Control Optim. 1983;21:462‐471. · Zbl 0513.93047
[27] SontagED. A ‘universal’ constructive of Artstein’s theorem on nonlinear stabilization. Syst Control Lett. 1989;12:542‐550.
[28] WuJL. Simultaneous H_∞ control for nonlinear systems. IEEE Trans Autom Control. 2009;54(3):606‐610. · Zbl 1367.93188
[29] IsidoriA. H_∞ control via measurement feedback for affine nonlinear systems. Int J Robust Nonlinear Control. 1994;4(4):553‐574. · Zbl 0806.93016
[30] AstolfiA. Singular H_∞ control for nonlinear systems. Int J Robust Nonlinear Control. 1997;7:727‐740. · Zbl 0878.93022
[31] MaasWCA, van derSchaftAJ. Singular nonlinear H_∞ optimal control problem. Int J Robust Nonlinear Control, 1996; 6: 669-689. · Zbl 0861.93007
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.