Design of saturating state feedback control laws for discrete‐time linear parameter varying systems through homogeneous polynomial parameter‐dependent functions
This article investigates the local stabilization problem for the class of discrete‐time linear parameter varying (LPV) systems subject to saturating actuators. The main contributions are new convex conditions for synthesizing rational parameter‐dependent state feedback gain controllers, ensuring th...
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| Published in | International journal of robust and nonlinear control Vol. 31; no. 14; pp. 6585 - 6601 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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| Abstract | This article investigates the local stabilization problem for the class of discrete‐time linear parameter varying (LPV) systems subject to saturating actuators. The main contributions are new convex conditions for synthesizing rational parameter‐dependent state feedback gain controllers, ensuring the local stability of the closed‐loop system for a set of initial conditions. We propose two design conditions for the local stabilization of the considered class of systems, which may lead to complementary results. We use a homogeneous polynomial parameter‐dependent (HPPD) based structure on the matrices variables. Thanks to a level set defined from an HPPD based Lyapunov function, we get less conservative estimates of the region of attraction. We provide a generalization of previous formulations from the literature to compute the intersection of parameter‐dependent ellipsoidal sets through finite‐dimensional conditions. The parameter‐dependent controller gains may assume rational structures on the time‐varying parameters, yielding better estimates of the region of attraction, as well as a broad set of stabilizable systems. Two examples illustrate the numerical aspects of the proposed conditions and give the reader a perspective of the relations concerning the conservatism and the degree of the HPPD functions. |
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| AbstractList | This article investigates the local stabilization problem for the class of discrete‐time linear parameter varying (LPV) systems subject to saturating actuators. The main contributions are new convex conditions for synthesizing rational parameter‐dependent state feedback gain controllers, ensuring the local stability of the closed‐loop system for a set of initial conditions. We propose two design conditions for the local stabilization of the considered class of systems, which may lead to complementary results. We use a homogeneous polynomial parameter‐dependent (HPPD) based structure on the matrices variables. Thanks to a level set defined from an HPPD based Lyapunov function, we get less conservative estimates of the region of attraction. We provide a generalization of previous formulations from the literature to compute the intersection of parameter‐dependent ellipsoidal sets through finite‐dimensional conditions. The parameter‐dependent controller gains may assume rational structures on the time‐varying parameters, yielding better estimates of the region of attraction, as well as a broad set of stabilizable systems. Two examples illustrate the numerical aspects of the proposed conditions and give the reader a perspective of the relations concerning the conservatism and the degree of the HPPD functions. |
| Author | Figueiredo, Larissa S. Lacerda, Márcio J. Leite, Valter J. S. |
| Author_xml | – sequence: 1 givenname: Larissa S. surname: Figueiredo fullname: Figueiredo, Larissa S. organization: CEFET‐MG, Campus Divinópolis – sequence: 2 givenname: Márcio J. orcidid: 0000-0001-8487-3535 surname: Lacerda fullname: Lacerda, Márcio J. organization: Federal University of São João del‐Rei ‐ UFSJ – sequence: 3 givenname: Valter J. S. orcidid: 0000-0002-8177-4547 surname: Leite fullname: Leite, Valter J. S. email: valter@ieee.org organization: CEFET‐MG, Campus Divinópolis |
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| Cites_doi | 10.1002/rnc.558 10.1109/CDC.2004.1430334 10.1080/00207721.2014.911389 10.1007/978-1-4614-1833-7 10.1080/00207170310001654174 10.1016/j.automatica.2017.02.006 10.1002/rnc.4746 10.1016/j.ifacol.2018.11.156 10.1007/s40435-013-0039-4 10.1016/S0167-6911(01)00118-9 10.1002/rnc.1507 10.1137/1.9781611970777 10.1109/TAC.2004.841128 10.1016/j.jfranklin.2020.04.019 10.1002/rnc.3846 10.1007/978-3-642-36110-4 10.1016/j.automatica.2009.07.015 10.1109/TAC.2016.2580662 10.1007/s12555-017-0526-z 10.1016/j.ifacol.2018.11.154 10.1016/j.sysconle.2004.11.016 10.1016/S0005-1098(03)00069-4 10.1016/j.sysconle.2005.05.003 10.1109/9.486638 10.1016/j.automatica.2009.10.022 10.1109/FUZZ-IEEE.2018.8491459 10.1080/10556789908805766 10.1109/9.262058 10.1007/978-0-85729-941-3 10.1016/j.sysconle.2010.11.006 10.1109/ACC.2007.4282551 10.1016/j.automatica.2006.08.024 10.1007/s00034-011-9292-y 10.1016/j.automatica.2016.01.053 10.1109/TAC.2007.914221 10.1145/3323925 |
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| SubjectTerms | Actuators Attraction Control stability Estimates Feedback control Initial conditions Liapunov functions LPV systems Parameter estimation polynomially dependent Lyapunov functions Polynomials rational controllers saturating actuators Stabilization State feedback Time varying control systems |
| Title | Design of saturating state feedback control laws for discrete‐time linear parameter varying systems through homogeneous polynomial parameter‐dependent functions |
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