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Automation and Remote Control
Erschienen in: Automation and Remote Control 11/2023

01.11.2023 | LINEAR SYSTEMS

Robust Stability of Differential-Algebraic Equations under Parametric Uncertainty

verfasst von: A. A. Shcheglova

Erschienen in: Automation and Remote Control | Ausgabe 11/2023

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Abstract

This paper considers linear differential-algebraic equations (DAEs) representing a system of ordinary differential equations with an identically singular matrix at the derivative in the domain of its definition. The matrix coefficients of DAEs are assumed to depend on the uncertain parameters belonging to a given admissible set. For the parametric family under consideration, structural forms with separate differential and algebraic parts are built. As is demonstrated below, the robust stability of the DAE family is equivalent to the robust stability of its differential subsystem. For the structure of perturbations, sufficient conditions are established under which the separation of DAEs into the algebraic and differential components preserves the original type of functional dependence on the uncertain parameters. Sufficient conditions for robust stability are obtained by constructing a quadratic Lyapunov function.
Vorheriger Artikel Interval Observers for Continuous-Time Systems with Parametric Uncertainties
Nächster Artikel Pattern Bifurcation in a Nonlocal Erosion Equation

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Fußnoten
1
The matrix Qr is quasi-diagonal: the blocks listed in curly brackets stand on the principal diagonal and all other elements are zero.
 
Literatur
1.
Brenan, K.E., Campbell, S.L., and Petzold, L.R., Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, Classics in Applied Mathematics, vol. 14, Philadelphia: SIAM, 1996.
2.
Polyak, B.T. and Shcherbakov, P.S., Robastnaya ustoichivost' i upravlenie (Robust Stability and Control), Moscow: Nauka, 2002.
3.
Chistyakov, V.F. and Shcheglova, A.A., Izbrannye glavy teorii algebro-differentsial’nykh sistem (Selected Chapters of the Theory of Algebraic-Differential Systems), Novosibirsk: Nauka, 2003.
4.
Byers, R. and Nichols, N.K., On the Stability Radius of a Generalized State-Space System, Linear Algebra Appl., 1993, vol. 188-189, pp. 113–134.MathSciNetCrossRef
5.
Qiu, L. and Davison, E.J., The Stability Robustness of Generalized Eigenvalues, IEEE Trans. Automat. Control, 1992, vol. 37, pp. 886–891.MathSciNetCrossRef
6.
Chyan, C.J., Du, N.H., and Linh, V.H., On Data-Dependence of Exponential Stability and the Stability Radii for Linear Time-Varying Differential-Algebraic Systems, J. Differ. Equat., 2008, vol. 245, pp. 2078–2102.ADSMathSciNetCrossRef
7.
Du, N.H. and Linh, V.H., Stability Radii for Linear Time-Varying Differential-Algebraic Equations with Respect to Dynamics Perturbations, J. Differ. Equat., 2006, vol. 230, pp. 579–599.ADSMathSciNetCrossRef
8.
Fang, C.-H. and Chang, F.-R., Analysis of Stability Robustness for Generalized State-Space Systems with Structured Perturbations, Systems Control Lett., 1993, vol. 21, pp. 109–114.MathSciNetCrossRef
9.
Lee, L., Fang, C.-H., and Hsieh, J.-G., Exact Unindirectional Perturbation Bounds for Robustness of Uncertain Generalized State-Space Systems: Continuous-Time Cases, Automatica, 1997, vol. 33, pp. 1923–1927.CrossRef
10.
De Teran, F., Dopico, F.M., and Moro, J., First Order Spectral Perturbation Theory of Square Singular Matrix Pencil, Linear Algebra Appl., 2008, vol. 429, pp. 548–576.MathSciNetCrossRef
11.
Linh, V.H. and Mehrmann, V., Lyapunov, Bohl and Sacker-Sell Spectral Intervals for Differential-Algebraic Equations, J. Dyn. Differ. Equat., 2009, vol. 21, pp. 153–194.MathSciNetCrossRef
12.
Lin, Ch., Lam, J., Wang, J., and Yang, G.-H., Analysis on Robust Stability for Interval Descriptor Systems, Syst. Control Lett., 2001, vol. 42, pp. 267–278.MathSciNetCrossRef
13.
Berger, T., Robustness of Stability of Time-Varying Index-1 DAEs, Math. Control Signals Syst., 2014, vol. 26, pp. 403–433.MathSciNetCrossRef
14.
Du, N.H., Linh, V.H., and Mehrmann, V., Robust Stability of Differential-Algebraic Equations, in Surveys in Differential-Algebraic Equations I., Ilchmann, A. and Reis, T., eds., Berlin–Heidelberg: Springer-Verlag, 2013.
15.
Barbosa, K., de Sousa, C., and Coutinho, D., Robust Admissibility and H ∞ Performance of Time-Varying Descriptor Systems, Proc. 10th IEEE Int. Conf. on Control Autom., Hangzhou, China, 2013, pp. 1138–1143.
16.
Bara, G.I., Robust Analysis and Control of Parameter-Dependent Uncertain Descriptor Systems, Syst. Control Lett., 2011, vol. 60, no. 5, pp. 356–364.MathSciNetCrossRef
17.
Gao, L., Chen, W., and Sun, Y., On Robust Admissibility Condition for Descriptor Systems with Convex Polytopic Uncertainty, Proc. 2003 Amer. Control Conf., Denver, USA, 2003, vol. 6, pp. 5083–5088.
18.
Xing, S., Zhang, Q., and Zhu, B., Mean-Square Admissibility for Stochastic T-S Fuzzy Singular Systems Based on Extended Quadratic Lyapunov Function Approach, Fuzzy Sets Syst., 2017, vol. 307, pp. 99–114.MathSciNetCrossRef
19.
20.
Taniguchi, T., Tanaka, K., Yamafuji, K., and Wang, H.O., Fuzzy Descriptor Systems: Stability Analysis and Design via LMIs, Proc. 1999 Amer. Control Conf., San Diego, USA, 1999, vol. 3, pp. 1827–1831.
21.
Dong, X.-Z., Admissibility Analysis of Linear Singular Systems via a Delta Operator Method, Int. J. Syst. Sci., 2014, vol. 45, pp. 2366–2375.MathSciNetCrossRef
22.
Shcheglova, A.A. and Kononov, A.D., Robust Stability of Differential-Algebraic Equations with an Arbitrary Unsolvability Index, Autom. Remote Control, 2017, vol. 78, no. 5, pp. 798–814.MathSciNetCrossRef
23.
Shcheglova, A.A. and Kononov, A.D., Stability of Differential-Algebraic Equations under Uncertainty, Differential Equations, 2018, vol. 54, no. 7, pp. 860–869.MathSciNetCrossRef
24.
Demidovich, B.P., Lektsii po matematicheskoi teorii ustoichivosti (Lectures on the Mathematical Theory of Stability), Moscow: Nauka, 1967.
25.
Campbell, S.L. and Petzold, L.R., Canonical Forms and Solvable Singular Systems of Differential Equations, SIAM J. Alg. Discrete Methods, 1983, vol. 4, pp. 517–521.MathSciNetCrossRef
26.
Gantmacher, F.R., Theory of Matrices, New York: Chelsea Publishing, 1959.
Metadaten
Titel
Robust Stability of Differential-Algebraic Equations under Parametric Uncertainty
verfasst von
A. A. Shcheglova
Publikationsdatum
01.11.2023
Verlag
Pleiades Publishing
Erschienen in
Automation and Remote Control / Ausgabe 11/2023
Print ISSN: 0005-1179
Elektronische ISSN: 1608-3032
DOI
https://doi.org/10.1134/S0005117923110061

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