An analysis and design method for a class of nonlinear systems with nested saturations. (English) Zbl 1353.93054
Summary: This paper is concerned with the analysis and design of a class of nonlinear systems subject to nested saturations. The proposed controller incorporates both an extended state observer (ESO), which is utilised to estimate the nonlinear dynamics of the plant, as well as a set of observer-based feedbacks. We first present analysis results for systems with nonlinear ESOs and show that local stabilisation can be achieved in a region including the origin. Then, in the case that the ESO is in linear form (LESO), the conditions for determining the estimate of the domain of attraction of the resulting closed-loop system are formulated as a convex optimisation problem. A linear matrix inequality based algorithm is then established to design the feedback gains and the LESO gain. An illustrative example is given to show the effectiveness of the proposed approach.
MSC:
| 93C10 | Nonlinear systems in control theory |
| 93B51 | Design techniques (robust design, computer-aided design, etc.) |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 93B07 | Observability |
| 93D15 | Stabilization of systems by feedback |
References:
| [1] | DOI: 10.1109/TAC.2002.800764 · Zbl 1364.93272 · doi:10.1109/TAC.2002.800764 |
| [2] | DOI: 10.1016/S0167-6911(02)00246-3 · Zbl 1106.93313 · doi:10.1016/S0167-6911(02)00246-3 |
| [3] | DOI: 10.1137/1.9781611970777 · Zbl 0816.93004 · doi:10.1137/1.9781611970777 |
| [4] | DOI: 10.1109/9.981734 · Zbl 1364.93612 · doi:10.1109/9.981734 |
| [5] | DOI: 10.1109/9.486637 · Zbl 0857.93048 · doi:10.1109/9.486637 |
| [6] | DOI: 10.1049/iet-cta.2008.0314 · doi:10.1049/iet-cta.2008.0314 |
| [7] | DOI: 10.1109/TAC.2008.2006821 · Zbl 1367.93498 · doi:10.1109/TAC.2008.2006821 |
| [8] | DOI: 10.1109/TAC.2004.841128 · Zbl 1365.93443 · doi:10.1109/TAC.2004.841128 |
| [9] | DOI: 10.1109/TAC.2003.811265 · Zbl 1364.93634 · doi:10.1109/TAC.2003.811265 |
| [10] | DOI: 10.1016/j.sysconle.2011.03.008 · Zbl 1225.93056 · doi:10.1016/j.sysconle.2011.03.008 |
| [11] | DOI: 10.1016/j.sysconle.2011.11.003 · Zbl 1256.93045 · doi:10.1016/j.sysconle.2011.11.003 |
| [12] | DOI: 10.1109/TIE.2008.2011621 · doi:10.1109/TIE.2008.2011621 |
| [13] | DOI: 10.1007/978-1-4612-0205-9 · doi:10.1007/978-1-4612-0205-9 |
| [14] | DOI: 10.1109/TAC.2006.884942 · Zbl 1366.93439 · doi:10.1109/TAC.2006.884942 |
| [15] | DOI: 10.1016/j.automatica.2015.06.012 · Zbl 1326.93073 · doi:10.1016/j.automatica.2015.06.012 |
| [16] | Khalil H.K., Nonlinear systems, 3. ed. (2002) |
| [17] | DOI: 10.1002/acs.1065 · Zbl 1163.93353 · doi:10.1002/acs.1065 |
| [18] | DOI: 10.1016/j.automatica.2013.04.005 · Zbl 1364.93024 · doi:10.1016/j.automatica.2013.04.005 |
| [19] | DOI: 10.1016/0167-6911(93)90033-3 · Zbl 0788.93075 · doi:10.1016/0167-6911(93)90033-3 |
| [20] | DOI: 10.1109/TAC.2010.2069612 · Zbl 1368.93631 · doi:10.1109/TAC.2010.2069612 |
| [21] | DOI: 10.1016/j.automatica.2012.11.018 · Zbl 1267.93054 · doi:10.1016/j.automatica.2012.11.018 |
| [22] | DOI: 10.1007/978-0-85729-941-3 · Zbl 1279.93004 · doi:10.1007/978-0-85729-941-3 |
| [23] | DOI: 10.1109/TAC.2006.878743 · Zbl 1366.93531 · doi:10.1109/TAC.2006.878743 |
| [24] | DOI: 10.1109/9.362894 · Zbl 0818.93062 · doi:10.1109/9.362894 |
| [25] | DOI: 10.1016/j.automatica.2010.03.016 · Zbl 1194.93185 · doi:10.1016/j.automatica.2010.03.016 |
| [26] | DOI: 10.1109/TAC.2013.2248256 · Zbl 1369.93257 · doi:10.1109/TAC.2013.2248256 |
| [27] | DOI: 10.1109/TAC.2010.2047033 · Zbl 1368.93668 · doi:10.1109/TAC.2010.2047033 |
| [28] | DOI: 10.1080/002071700414211 · Zbl 0992.93033 · doi:10.1080/002071700414211 |
| [29] | DOI: 10.1109/TAC.2011.2175071 · Zbl 1369.93707 · doi:10.1109/TAC.2011.2175071 |
| [30] | DOI: 10.1016/j.sysconle.2013.06.012 · Zbl 1281.93064 · doi:10.1016/j.sysconle.2013.06.012 |
| [31] | DOI: 10.1016/j.automatica.2010.10.001 · Zbl 1207.93044 · doi:10.1016/j.automatica.2010.10.001 |
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.
