Some Remarks on the Complex Stability Radius of Differential-Algebraic Equations
Main Article Content
Abstract
Abstract. This paper is concerned with the robust stability of linear differential-algebraic equations (DAEs). A system of linear DAEs subjected to structured perturbation is considered. Computable formulas of the complex stability radius are given and analysed. A comparison of our formula to previous results is given.
Keywords: linear differential-algebraic equations, index of matrix pencil, asymptotic stability, structured perturbation, complex stability radius.
References
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[3] W. Zhu, L.R. Petzold. Asymptotic stability of linear delay differential-algebraic equations and numerical methods. Applied Numerical Mathematics, (24), 247-264, 1997
[4] D. Hinrichsen and A.J. Pritchard. Stability radii of linear systems. Systems Control Letters, (7), 1-10, 1986.
[5] D. Hinrichsen and A.J. Pritchard. Stability radii for structured perturbations and the alge¬braic Riccati equations. Systems Control Letters, (8), 105-113, 1986
[6] C.F. Van Loan. How near is a stable matrix to an unstable matrix? Contemp. Math., (47), 465-478, 1985.
[7] L. Qiu, E.J. Davison. The Stability Robustness of Generalized Eigenvalues. IEEE Transac¬tions on Automatic Control, (37, No.6), 886-891, 1992
[8] Ralph Byers, N.K. Nichols. On the Stability Radius of a Generalized State Space System. Linear Algebra and Its Applications, (188, 189),113-134, 1993.
[9] N.H. Du, Stability radii for differential-algebraic equations. Vietnam Journal Mathematics, (27), 379-382, 1999.
[10] N.H. Du, D.T. Lien, V.H. Linh. On Complex Stability Radii for Implicit Discrete Time Systems. Vietnam Journal of Mathematics, (31, No.4), 475-488, 2003.
[11] N.H.Du, V.H. Linh. Robust stability of implicit linear systems containing a small parameter in the leading term. IMA J. Mathematical Control Information, (23), 67-84, 2006.
[12] M. Bracke. On. stability radii of parametrized linear differential-algebraic systems. Ph.D. Thesis, University of Kaiserslautern, 2000.
[13] F. R. Gantmacher. The Theory of Matrices. Vols. I,II, AMS Chelsea Publishing, New York, 1974.
[14] Gene H. Golub, Charles F. Van Loan. Matrix Computations. The Johns Hopkins University Press, Baltimore and London, 1996.