Multiple Lyapunov functions approach to observer-based \(H_{\infty}\) control for switched systems. (English) Zbl 1278.93097
Summary: This article investigates the issue of \(H_{\infty}\) control for a class of continuous-time switched Lipschitz nonlinear systems. None of the individual subsystems is assumed to be stabilizable with \(H_{\infty}\) disturbance attenuation. Based on a Generalized Multiple Lyapunov Functions (GMLFs) approach, which removes the non-increasing requirement at switching points, a sufficient condition for the solvability of the \(H_{\infty}\) control problem under a state estimation-dependent switching law is presented. Observers, controllers and a switching law are simultaneously designed. As an extension, a sufficient condition for exponential stabilizability is also given.
MSC:
| 93B36 | \(H^\infty\)-control |
| 93D30 | Lyapunov and storage functions |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
Keywords:
switched systems; observer; \(H_{\infty}\) control; exponential stabilization; multiple Lyapunov functions; generalized multiple Lyapunov functions (GMLFs)References:
| [1] | DOI: 10.1007/3-540-45351-2_5 · doi:10.1007/3-540-45351-2_5 |
| [2] | DOI: 10.1080/00207170110086953 · Zbl 1101.93302 · doi:10.1080/00207170110086953 |
| [3] | Boyd S, Convex Optimisation with Engineering Applications, Lecture Notes (2001) |
| [4] | DOI: 10.1109/9.664150 · Zbl 0904.93036 · doi:10.1109/9.664150 |
| [5] | DOI: 10.1049/ip-cta:20040307 · doi:10.1049/ip-cta:20040307 |
| [6] | DOI: 10.1016/j.sysconle.2007.07.001 · Zbl 1129.93042 · doi:10.1016/j.sysconle.2007.07.001 |
| [7] | DOI: 10.1016/j.conengprac.2007.10.004 · doi:10.1016/j.conengprac.2007.10.004 |
| [8] | Feng G, Communications in Information and Systems 2 pp 245– (2002) · Zbl 1119.93321 · doi:10.4310/CIS.2002.v2.n3.a2 |
| [9] | DOI: 10.1109/81.983869 · Zbl 1368.93195 · doi:10.1109/81.983869 |
| [10] | DOI: 10.1049/ip-cta:20040306 · doi:10.1049/ip-cta:20040306 |
| [11] | DOI: 10.1002/rnc.1171 · Zbl 1127.93312 · doi:10.1002/rnc.1171 |
| [12] | DOI: 10.1016/S0005-1098(02)00267-4 · Zbl 1013.93045 · doi:10.1016/S0005-1098(02)00267-4 |
| [13] | DOI: 10.1007/978-1-4612-0017-8 · doi:10.1007/978-1-4612-0017-8 |
| [14] | Peleties, P and DeCarlo, R. 1991. Asymptotic Stability ofm-Switched Systems Using Lyapunov-like Functions. Proceedings of American Control Conference. 1991. pp.1679–1684. |
| [15] | Pettersson S, Proceedings of the 16th IFAC World Congress 1 pp 127– (2005) |
| [16] | DOI: 10.1080/0020717031000091432 · Zbl 1040.93034 · doi:10.1080/0020717031000091432 |
| [17] | DOI: 10.1016/j.automatica.2008.04.015 · Zbl 1152.93389 · doi:10.1016/j.automatica.2008.04.015 |
| [18] | DOI: 10.1080/00207720902974686 · Zbl 1175.93191 · doi:10.1080/00207720902974686 |
| [19] | DOI: 10.1080/00207721.2010.488763 · Zbl 1233.93094 · doi:10.1080/00207721.2010.488763 |
| [20] | DOI: 10.1049/iet-cta:20060502 · doi:10.1049/iet-cta:20060502 |
| [21] | DOI: 10.1016/j.sysconle.2007.06.012 · Zbl 1129.93006 · doi:10.1016/j.sysconle.2007.06.012 |
| [22] | DOI: 10.1016/j.automatica.2007.10.011 · Zbl 1283.93147 · doi:10.1016/j.automatica.2007.10.011 |
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.
