LMI approach to linear positive system analysis and synthesis
This paper is concerned with the analysis and synthesis of linear positive systems based on linear matrix inequalities (LMIs). We first show that the celebrated Perron–Frobenius theorem can be proved concisely by a duality-based argument. Again by duality, we next clarify a necessary and sufficient...
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| Published in: | Systems & control letters Vol. 63; pp. 50 - 56 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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01.01.2014
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| ISSN: | 0167-6911, 1872-7956 |
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| Abstract | This paper is concerned with the analysis and synthesis of linear positive systems based on linear matrix inequalities (LMIs). We first show that the celebrated Perron–Frobenius theorem can be proved concisely by a duality-based argument. Again by duality, we next clarify a necessary and sufficient condition under which a Hurwitz stable Metzler matrix admits a diagonal Lyapunov matrix with some identical diagonal entries as the solution of the Lyapunov inequality. This new result leads to an alternative proof of the recent result by Tanaka and Langbort on the existence of a diagonal Lyapunov matrix for the LMI characterizing the H∞ performance of continuous-time positive systems. In addition, we further derive a new LMI for the H∞ performance analysis where the variable corresponding to the Lyapunov matrix is allowed to be non-symmetric. We readily extend these results to discrete-time positive systems and derive new LMIs for the H∞ performance analysis and synthesis. We finally illustrate their effectiveness by numerical examples on robust state-feedback H∞ controller synthesis for discrete-time positive systems affected by parametric uncertainties. |
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| AbstractList | This paper is concerned with the analysis and synthesis of linear positive systems based on linear matrix inequalities (LMIs). We first show that the celebrated Perron-Frobenius theorem can be proved concisely by a duality-based argument. Again by duality, we next clarify a necessary and sufficient condition under which a Hurwitz stable Metzler matrix admits a diagonal Lyapunov matrix with some identical diagonal entries as the solution of the Lyapunov inequality. This new result leads to an alternative proof of the recent result by Tanaka and Langbort on the existence of a diagonal Lyapunov matrix for the LMI characterizing the H infinity H infinity performance of continuous-time positive systems. In addition, we further derive a new LMI for the H infinity H infinity performance analysis where the variable corresponding to the Lyapunov matrix is allowed to be non-symmetric. We readily extend these results to discrete-time positive systems and derive new LMIs for the H infinity H infinity performance analysis and synthesis. We finally illustrate their effectiveness by numerical examples on robust state-feedback H infinity H infinity controller synthesis for discrete-time positive systems affected by parametric uncertainties. This paper is concerned with the analysis and synthesis of linear positive systems based on linear matrix inequalities (LMIs). We first show that the celebrated Perron–Frobenius theorem can be proved concisely by a duality-based argument. Again by duality, we next clarify a necessary and sufficient condition under which a Hurwitz stable Metzler matrix admits a diagonal Lyapunov matrix with some identical diagonal entries as the solution of the Lyapunov inequality. This new result leads to an alternative proof of the recent result by Tanaka and Langbort on the existence of a diagonal Lyapunov matrix for the LMI characterizing the performance of continuous-time positive systems. In addition, we further derive a new LMI for the performance analysis where the variable corresponding to the Lyapunov matrix is allowed to be non-symmetric. We readily extend these results to discrete-time positive systems and derive new LMIs for the performance analysis and synthesis. We finally illustrate their effectiveness by numerical examples on robust state-feedback controller synthesis for discrete-time positive systems affected by parametric uncertainties. This paper is concerned with the analysis and synthesis of linear positive systems based on linear matrix inequalities (LMIs). We first show that the celebrated Perron–Frobenius theorem can be proved concisely by a duality-based argument. Again by duality, we next clarify a necessary and sufficient condition under which a Hurwitz stable Metzler matrix admits a diagonal Lyapunov matrix with some identical diagonal entries as the solution of the Lyapunov inequality. This new result leads to an alternative proof of the recent result by Tanaka and Langbort on the existence of a diagonal Lyapunov matrix for the LMI characterizing the H∞ performance of continuous-time positive systems. In addition, we further derive a new LMI for the H∞ performance analysis where the variable corresponding to the Lyapunov matrix is allowed to be non-symmetric. We readily extend these results to discrete-time positive systems and derive new LMIs for the H∞ performance analysis and synthesis. We finally illustrate their effectiveness by numerical examples on robust state-feedback H∞ controller synthesis for discrete-time positive systems affected by parametric uncertainties. |
| Author | Arzelier, Denis Ebihara, Yoshio Peaucelle, Dimitri |
| Author_xml | – sequence: 1 givenname: Yoshio surname: Ebihara fullname: Ebihara, Yoshio email: ebihara@kuee.kyoto-u.ac.jp organization: Department of Electrical Engineering, Kyoto University, Kyotodaigaku-Katsura, Nishikyo-ku, Kyoto 615-8510, Japan – sequence: 2 givenname: Dimitri surname: Peaucelle fullname: Peaucelle, Dimitri organization: LAAS-CNRS, Université de Toulouse, 7 Av. du Colonel Roche, 31077, Toulouse Cedex 4, France – sequence: 3 givenname: Denis surname: Arzelier fullname: Arzelier, Denis organization: LAAS-CNRS, Université de Toulouse, 7 Av. du Colonel Roche, 31077, Toulouse Cedex 4, France |
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| Cites_doi | 10.1109/TAC.2007.900857 10.1109/TAC.2007.899057 10.1080/03081087808817203 10.1109/TAC.2002.806652 10.1016/0167-6911(95)00063-1 10.1109/ACC.2012.6314755 10.1080/00207179.2013.797106 10.1016/j.laa.2008.06.037 10.1109/TAC.2011.2157394 10.1007/978-3-540-30560-6_2 10.1109/CDC.2011.6161293 10.1109/MSP.2005.1406483 10.1109/CDC.2012.6426312 10.1080/00207170210140212 |
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| Keywords | LMI Duality Positive system Diagonal Lyapunov matrix |
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| References | Rantzer (br000080) 1996; 28 Matsumura, Ebihara, Hagiwara (br000090) 2013; 26 Farina, Rinaldi (br000005) 2000 Y. Ebihara, Dual LMI approach to linear positive system analysis, in: Proc. The 12th International Conference on Control, Automation and Systems, ICCAS, 2012, pp. 887–891. Pillai, Suel, Cha (br000065) 2005; 2 Tanaka, Langbort (br000035) 2011; 56 Najson (br000050) 2013 de Oliveira, Geromel, Bernussou (br000095) 2002; 75 A. Rantzer, Distributed control of positive systems, in: Proc. Conference on Decision and Control, 2011, pp. 6608–6611. controller synthesis for positive systems and its robustness properties, in: Proc. American Control Conference, 2012, pp. 5992–5997. Balakrishnan, Vandenberghe (br000070) 2003; 48 Gurvits, Shorten, Mason (br000015) 2007; 52 Mason, Shorten (br000020) 2007; 52 Barker, Berman, Plemmons (br000085) 1978; 5 Kaczorek (br000010) 2001 Y. Ebihara, D. Peaucelle, D. Arzelier, Optimal Boyd, Balakrishnan (br000075) 2004 A. Rantzer, Optimizing positively dominated systems, in: Proc. Conference on Decision and Control, 2012, pp. 272–277. Shorten, Mason, King (br000025) 2009; 430 Shorten, Mason, Wulff (br000030) 2005; 3335 Tanaka (10.1016/j.sysconle.2013.11.001_br000035) 2011; 56 Pillai (10.1016/j.sysconle.2013.11.001_br000065) 2005; 2 Farina (10.1016/j.sysconle.2013.11.001_br000005) 2000 Shorten (10.1016/j.sysconle.2013.11.001_br000030) 2005; 3335 Rantzer (10.1016/j.sysconle.2013.11.001_br000080) 1996; 28 Mason (10.1016/j.sysconle.2013.11.001_br000020) 2007; 52 Shorten (10.1016/j.sysconle.2013.11.001_br000025) 2009; 430 Boyd (10.1016/j.sysconle.2013.11.001_br000075) 2004 Balakrishnan (10.1016/j.sysconle.2013.11.001_br000070) 2003; 48 Matsumura (10.1016/j.sysconle.2013.11.001_br000090) 2013; 26 Najson (10.1016/j.sysconle.2013.11.001_br000050) 2013 de Oliveira (10.1016/j.sysconle.2013.11.001_br000095) 2002; 75 Kaczorek (10.1016/j.sysconle.2013.11.001_br000010) 2001 Gurvits (10.1016/j.sysconle.2013.11.001_br000015) 2007; 52 Barker (10.1016/j.sysconle.2013.11.001_br000085) 1978; 5 10.1016/j.sysconle.2013.11.001_br000040 10.1016/j.sysconle.2013.11.001_br000060 10.1016/j.sysconle.2013.11.001_br000045 10.1016/j.sysconle.2013.11.001_br000055 |
| References_xml | – year: 2001 ident: br000010 article-title: Positive 1D and 2D Systems – volume: 52 start-page: 1099 year: 2007 end-page: 1103 ident: br000015 article-title: On the stability of switched positive linear systems publication-title: IEEE Trans. Automat. Control – volume: 56 start-page: 2218 year: 2011 end-page: 2223 ident: br000035 article-title: The bounded real lemma for internally positive systems and publication-title: IEEE Trans. Automat. Control – reference: Y. Ebihara, Dual LMI approach to linear positive system analysis, in: Proc. The 12th International Conference on Control, Automation and Systems, ICCAS, 2012, pp. 887–891. – year: 2000 ident: br000005 article-title: Positive Linear Systems: Theory and Applications – volume: 3335 start-page: 31 year: 2005 end-page: 45 ident: br000030 article-title: Convex cones, Lyapunov functions, and the stability of switched linear systems publication-title: Lecture Notes in Comput. Sci. – volume: 48 start-page: 30 year: 2003 end-page: 41 ident: br000070 article-title: Semidefinite programming duality and linear time-invariant systems publication-title: IEEE Trans. Automat. Control – volume: 52 start-page: 1346 year: 2007 end-page: 1349 ident: br000020 article-title: On linear copositive Lyapunov function and the stability of switched positive linear systems publication-title: IEEE Trans. Automat. Control – reference: A. Rantzer, Optimizing positively dominated systems, in: Proc. Conference on Decision and Control, 2012, pp. 272–277. – reference: Y. Ebihara, D. Peaucelle, D. Arzelier, Optimal – volume: 28 start-page: 7 year: 1996 end-page: 10 ident: br000080 article-title: On the Kalman–Yakubovich–Popov lemma publication-title: Syst. Control Lett. – volume: 430 start-page: 34 year: 2009 end-page: 40 ident: br000025 article-title: An alternative proof of the Barker, Berman, Plemmons (BBP) result on diagonal stability and extensions publication-title: Linear Algebra Appl. – year: 2013 ident: br000050 article-title: On the Kalman–Yakubovich–Popov lemma for discrete-time positive linear systems: a novel simple proof and some related results publication-title: Int. J. Control – volume: 5 start-page: 249 year: 1978 end-page: 256 ident: br000085 article-title: Positive diagonal solutions to the Lyapunov equations publication-title: Linear Multilinear Algebra – reference: A. Rantzer, Distributed control of positive systems, in: Proc. Conference on Decision and Control, 2011, pp. 6608–6611. – volume: 2 start-page: 62 year: 2005 end-page: 75 ident: br000065 article-title: The Perron–Frobenius theorem: some of its applications publication-title: IEEE Signal Process. Mag. – year: 2004 ident: br000075 article-title: Convex Optimization – reference: -controller synthesis for positive systems and its robustness properties, in: Proc. American Control Conference, 2012, pp. 5992–5997. – volume: 75 start-page: 666 year: 2002 end-page: 679 ident: br000095 article-title: Extended publication-title: Int. J. Control – volume: 26 start-page: 45 year: 2013 end-page: 51 ident: br000090 article-title: LMI-based stability and publication-title: Trans. Inst. Syst. Control Inf. Eng. – volume: 52 start-page: 1346 issue: 7 year: 2007 ident: 10.1016/j.sysconle.2013.11.001_br000020 article-title: On linear copositive Lyapunov function and the stability of switched positive linear systems publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2007.900857 – volume: 52 start-page: 1099 issue: 6 year: 2007 ident: 10.1016/j.sysconle.2013.11.001_br000015 article-title: On the stability of switched positive linear systems publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2007.899057 – volume: 5 start-page: 249 issue: 4 year: 1978 ident: 10.1016/j.sysconle.2013.11.001_br000085 article-title: Positive diagonal solutions to the Lyapunov equations publication-title: Linear Multilinear Algebra doi: 10.1080/03081087808817203 – volume: 48 start-page: 30 issue: 1 year: 2003 ident: 10.1016/j.sysconle.2013.11.001_br000070 article-title: Semidefinite programming duality and linear time-invariant systems publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2002.806652 – volume: 28 start-page: 7 year: 1996 ident: 10.1016/j.sysconle.2013.11.001_br000080 article-title: On the Kalman–Yakubovich–Popov lemma publication-title: Syst. Control Lett. doi: 10.1016/0167-6911(95)00063-1 – ident: 10.1016/j.sysconle.2013.11.001_br000045 doi: 10.1109/ACC.2012.6314755 – year: 2000 ident: 10.1016/j.sysconle.2013.11.001_br000005 – year: 2013 ident: 10.1016/j.sysconle.2013.11.001_br000050 article-title: On the Kalman–Yakubovich–Popov lemma for discrete-time positive linear systems: a novel simple proof and some related results publication-title: Int. J. Control doi: 10.1080/00207179.2013.797106 – year: 2001 ident: 10.1016/j.sysconle.2013.11.001_br000010 – volume: 430 start-page: 34 year: 2009 ident: 10.1016/j.sysconle.2013.11.001_br000025 article-title: An alternative proof of the Barker, Berman, Plemmons (BBP) result on diagonal stability and extensions publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2008.06.037 – volume: 26 start-page: 45 issue: 1 year: 2013 ident: 10.1016/j.sysconle.2013.11.001_br000090 article-title: LMI-based stability and H∞ performance analysis of discrete-time positive systems publication-title: Trans. Inst. Syst. Control Inf. Eng. – volume: 56 start-page: 2218 issue: 9 year: 2011 ident: 10.1016/j.sysconle.2013.11.001_br000035 article-title: The bounded real lemma for internally positive systems and H-infinity structured static state feedback publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2011.2157394 – volume: 3335 start-page: 31 year: 2005 ident: 10.1016/j.sysconle.2013.11.001_br000030 article-title: Convex cones, Lyapunov functions, and the stability of switched linear systems publication-title: Lecture Notes in Comput. Sci. doi: 10.1007/978-3-540-30560-6_2 – ident: 10.1016/j.sysconle.2013.11.001_br000060 – ident: 10.1016/j.sysconle.2013.11.001_br000040 doi: 10.1109/CDC.2011.6161293 – volume: 2 start-page: 62 issue: 2 year: 2005 ident: 10.1016/j.sysconle.2013.11.001_br000065 article-title: The Perron–Frobenius theorem: some of its applications publication-title: IEEE Signal Process. Mag. doi: 10.1109/MSP.2005.1406483 – year: 2004 ident: 10.1016/j.sysconle.2013.11.001_br000075 – ident: 10.1016/j.sysconle.2013.11.001_br000055 doi: 10.1109/CDC.2012.6426312 – volume: 75 start-page: 666 year: 2002 ident: 10.1016/j.sysconle.2013.11.001_br000095 article-title: Extended H2 and H∞ norm characterizations and controller parametrizations for discrete-time systems publication-title: Int. J. Control doi: 10.1080/00207170210140212 |
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| SubjectTerms | Automatic Control Engineering Computer Science Control systems Diagonal Lyapunov matrix Duality Inequalities Linear matrix inequalities LMI Mathematical models Positive system Synthesis Systems analysis Theorems Uncertainty |
| Title | LMI approach to linear positive system analysis and synthesis |
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