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Stabilization and passification of uncertain systems via static output feedback

Pavel Pakshin, Dimitri Peaucelle
2009 2009 IEEE International Conference on Control Applications  
Yet, this control strategy, also called passivity-based adaptive control, needs to be applied for the system to be passifiable.  ...  The paper is devoted to the search of such linear combinations with practical efficient algorithms. Results are discussed in detail for an uncertain time-varying aircraft control example.  ...  Based on the upper considerations, the following heuristic algorithm is proposed for robust stabilizing static output-feedback design 2-For this choice of λ apply Johnson's algorithm [12] and get matrices  ... 
doi:10.1109/cca.2009.5281026 dblp:conf/IEEEcca/PakshinP09 fatcat:hlm5yoopbbajvd27nurfihu7by

ELLIPSOIDAL SETS FOR STATIC OUTPUT FEEDBACK

Dimitri Peaucelle, Denis Arzelier, Regis Bertrand
2002 IFAC Proceedings Volumes  
The static output feedback synthesis for LTI systems is considered.  ...  It is shown to have analogies with robust analysis, in particular the existence of an output feedback gain is equivalent to the existence of some quadratic separator.  ...  This section is devoted to the static output feedback (SOF) stabilisability of linear time invariant (LTI), continuous-time systems.  ... 
doi:10.3182/20020721-6-es-1901.00195 fatcat:vllimbzl6rev5a2vzph5wpirbm

LMI conditions for robust adaptive control of MIMO LTI systems1

Dimitri Peaucelle, Alexander Fradkov
2007 IFAC Proceedings Volumes  
Passification-based direct adaptive control is considered for polytopic uncertain linear time-invariant multi-input multi-output systems.  ...  Linear Matrix Inequality based results are provided to guarantee that the adaptive algorithm passifies the system whatever the uncertain parameters in some given set.  ...  Theorem 1 The closed-loop system (1) with static feedback u = F y + v is strictly passive with respect to the signals v, z = Gy +Dv if and only if there exist a symmetric positive-definite matrix P > 0  ... 
doi:10.3182/20070829-3-ru-4911.00036 fatcat:xzzdhcmrefa2zl2gtpgxogxbtu

A cone complementarity linearization algorithm for static output-feedback and related problems

L. El Ghaoui, F. Oustry, M. AitRami
1997 IEEE Transactions on Automatic Control  
This paper describes a linear matrix inequality (LMI)-based algorithm for the static and reduced-order output-feedback synthesis problems of nth-order linear time-invariant (LTI) systems with nu (respectively  ...  , n y ) independent inputs (respectively, outputs).  ...  ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for their very helpful comments.  ... 
doi:10.1109/9.618250 fatcat:wqwmxfrsmzd3bnugawfznhe5ce

Fixed-order control of LTI systems subject to polytopic uncertainty via the concept of Strictly Positive Realness

Mahdieh S. Sadabadi, Alireza Karimi
2015 2015 American Control Conference (ACC)  
The proposed method is based on the concept of Strictly Positive Realness (SPRness) of a transfer function depending on a parameter-dependent gain.  ...  To convert the problem to a set of LMI conditions, the parameterdependent gain is determined a priori by means of a parameterdependent state feedback controller.  ...  Recently, several slack variable-based approaches to fixedorder controller design of polytopic systems, which rely on the concept of Strictly Positive Realness (SPRness) of transfer functions, have been  ... 
doi:10.1109/acc.2015.7171172 dblp:conf/amcc/SadabadiK15 fatcat:bx5lwgh2trhdpiugv6aadj6s5u

The discrete-time tracking problem with H∞ model matching approach plus integral control

Murat Akın, Tankut Acarman, N. Mastorakis, V. Mladenov, A. Bulucea
2019 MATEC Web of Conferences  
In this study, the discrete-time H∞ model matching problem with integral control by using 2 DOF static output feedback is presented. First, the motivation and the problem is stated.  ...  In following, the discrete-time H∞ MMP via LMI approach is derived as the main result.  ...  output feedback controller K=[L M]R mx2m exists for the discrete-time H∞ MMP with integral control and the closed-loop system is internally stable if and only if there is a matrix From the Bounded Real  ... 
doi:10.1051/matecconf/201929201018 fatcat:5ortsp47d5bitbkewizyh6arze

From static output feedback to structured robust static output feedback: A survey

Mahdieh S. Sadabadi, Dimitri Peaucelle
2016 Annual Reviews in Control  
This paper reviews the vast literature on static output feedback design for linear time-invariant systems including classical results and recent developments.  ...  In particular, we focus on static output feedback synthesis with performance specifications, structured static output feedback, and robustness.  ...  To these cases when the static output feedback design may be solved via one convex LMI, we add the following result from [18] that is also purely LMI, but based on three steps.  ... 
doi:10.1016/j.arcontrol.2016.09.014 fatcat:yo5k6hvsvfdgbnzufu7rmof4re

Robust Static Output Feedback Stabilization for Polytopic Uncertain Systems: Improving the Guaranteed Performance Bound

D. Arzelier, D. Peaucelle, S. Salhi
2003 IFAC Proceedings Volumes  
A new sufficient condition of robust stabilizability via static output feedback is proposed for polytopic uncertain systems.  ...  It is based on a new parameterization of all static output feedback stabilizing gains and uses parameter-dependent Lyapunov functions to systematically reduce conservatism of the usual quadratic stability  ...  via static output feedback.  ... 
doi:10.1016/s1474-6670(17)35701-4 fatcat:e63taoivljfsjl76g7cjt7zly4

Structured adaptive control for solving LMIs

Alexandru-Razvan Luzi, Alexander L. Fradkov, Jean-Marc Biannic, Dimitri Peaucelle
2013 IFAC Proceedings Volumes  
The paper exposes one such continuous-time method for solving linear matrix inequalities. The proposed differential equations are those of an adaptive control feedback loop on an LTI system.  ...  It for example reads as requiring the feedback gain to be symmetric when time goes to infinity. Point-wise global stability is proved with quadratic Lyapunov functions.  ...  loop system strictly passive with respect to inputs w and outputs z.  ... 
doi:10.3182/20130703-3-fr-4038.00075 fatcat:yne4jy6thjaufjgixowg2aog4a

Robust adaptive -gain control of polytopic MIMO LTI systems — LMI results

Dimitri Peaucelle, Alexander Fradkov
2008 Systems & control letters (Print)  
Passification-based direct adaptive control is considered for polytopic uncertain linear time-invariant multi-input multi-output systems.  ...  Moreover, it proves to be not worse than computable parameter-dependent static output-feedback controls with respect to L2 gain attenuation. A simple academic example illustrates the results.  ...  Equivalently it corresponds to the existence of a static output-feedback u = F y + w P such that the closed-loop from w P to z P is strictly passive (the open-loop system is sometimes called almost strictly  ... 
doi:10.1016/j.sysconle.2008.04.005 fatcat:jv75dz5pgvb6bj6nklkcvpk27e

Revisiting and Generalizing the Dual Iteration for Static and Robust Output-Feedback Synthesis [article]

Tobias Holicki, Carsten W. Scherer
2020 arXiv   pre-print
The dual iteration was introduced in a conference paper in 1997 by Iwasaki as an iterative and heuristic procedure for the challenging and non-convex design of static output-feedback controllers.  ...  Exemplary, we extend the dual iteration to the multi-objective design of static output-feedback H_∞-controllers, which guarantee that the closed-loop poles are contained in an a priori specified generalized  ...  The dual iteration for static output-feedback ∞ -design with generalized stability regions is explicitly stated as follows. Algorithm 2.  ... 
arXiv:2007.00965v1 fatcat:7rvrqgcw4fchvgw3irb6x45p2u

Positive polynomial matrices and improved LMI robustness conditions

Didier Henrion, Denis Arzelier, Dimitri Peaucelle
2003 Automatica  
Recently several new LMI conditions for stability of linear systems have been proposed, introducing additional slack variables to reduce the gap between conservative convex quadratic stability conditions  ...  In this paper we show that these improved LMI conditions can be derived with the help of some basic results on positive polynomial matrices, providing a clear interpretation of the role of the additional  ...  ACKNOWLEDGMENTS Thanks to Jos Sturm for providing beta versions of Se-DuMi 1.04 and 1.05. Comments by Michal Kvasnica and Gianni Bianchini were also appreciated.  ... 
doi:10.1016/s0005-1098(03)00129-8 fatcat:n3vdzsqkxzbjvozwlrvewc6thy

POSITIVE POLYNOMIAL MATRICES AND IMPROVED LMI ROBUSTNESS CONDITIONS

Didier Henrion, Denis Arzelier, Dimitri Peaucelle
2002 IFAC Proceedings Volumes  
Recently several new LMI conditions for stability of linear systems have been proposed, introducing additional slack variables to reduce the gap between conservative convex quadratic stability conditions  ...  In this paper we show that these improved LMI conditions can be derived with the help of some basic results on positive polynomial matrices, providing a clear interpretation of the role of the additional  ...  ACKNOWLEDGMENTS Thanks to Jos Sturm for providing beta versions of Se-DuMi 1.04 and 1.05. Comments by Michal Kvasnica and Gianni Bianchini were also appreciated.  ... 
doi:10.3182/20020721-6-es-1901.00362 fatcat:2k5mgzptqjgtrl3e7cyhbybarm

Simultaneous stabilization via static output feedback and state feedback

Yong-Yan Cao, You-Xian Sun, J. Lam
1999 IEEE Transactions on Automatic Control  
Some necessary and sufficient conditions for simultaneous stabilizability of r r r strictly proper multi-input/multi-output (MIMO) plants via static output feedback and state feedback are obtained in the  ...  A heuristic iterative algorithm based on the linear matrix inequality (LMI) technique is presented to solve the coupled matrix inequalities.  ...  ACKNOWLEDGMENT The authors would like to thank the Associate Editor and anonymous reviewers for their constructive comments and suggestions.  ... 
doi:10.1109/9.769390 fatcat:r3nkfimmgrcqlecfilt3ujnfnm

An iterative Newton's method for output-feedback LQR design for large-scale systems with guaranteed convergence

Adrian Ilka, Nikolce Murgovski, Jonas Sjoberg
2019 2019 18th European Control Conference (ECC)  
The proposed iterative method has a guaranteed convergence from an initial Lyapunov matrix, obtained for any stabilizing statefeedback gain, to a stabilizing output-feedback solution.  ...  The paper proposes a novel iterative outputfeedback control design procedure, with necessary and sufficient stability conditions, for linear time-invariant systems within the linear quadratic regulator  ...  The system (2) is said to be static output- feedback stabilizable if and only if there exist a real matrix F ∈ R nu×ny such that A − BF C is stable. Theorem 1.  ... 
doi:10.23919/ecc.2019.8795752 dblp:conf/eucc/IlkaMS19 fatcat:2hbl4azcw5b2xcjxgurq5ju2ae
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