Abstract
A diamond-type family of quasipolynomials, for which vertex stability results hold, is presented. Both delay independent and delay-dependent stability conditions are given. In the first case, it suffices to check for the stability of a finite testing set of multivariate polynomials. While in the other one, it is also needed to check the stability of several edge sub-families of quasipolynomials.
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References
Barmish, B. R. (1994). New tools for robustness of linear systems. MacMillan Publishing Co.
Barmish B.R., Tempo R., Hollot C.V., Kang H.I. (1992). An extreme point results for robust stability of a diamond of polynomials. IEEE Transactions on Automatic Control AC-37: 1460–1462
Basu S. (1990). On boundary implications of stability and positivity properties of multidimensional systems. Proceedings of IEEE 78, 614–626
Bellman R., Cooke K.L. (1963). Differential-difference equations. New York, Academic
Bose, N. K. (1982). Applied multidimensional systems theory. Van Nostrand Reinhold Company.
Bose N.K. (1996). Edge property from end points for scattering hurwitz polynomials. Automatica 32(4): 655–657
Kharitonov V.L. (1978). Asymptotic stability of an equilibrium position of a family of systems of linear differential equations. Differentsial’nie Uravneniya 14, 2086–2088
Kharitonov V.L., Torres Muñoz J.A. (1999). Robust stability of multivariate polynomials part 1: small coefficient perturbations. Multidimensional Systems and Signal Processing 10, 7–20
Kharitonov V.L., Torres Muñoz J.A. (2002). Recent results on the stability of multivariate polynomials. IEEE Transactions on Circuits and Systems 1: Fundamental Theory and Applications 49(6): 715–724
Kharitonov V.L., Torres Muñoz J.A., Ortiz-Moctezuma B. (2003). Polytopic families of Quasi-Polynomials: Vertex-type stability conditions. IEEE Transactions on Circuits and Systems 1: Fundamental Theory and Applications 50(11): 1413–1420
Kharitonov V.L., Torres Muñoz J.A., Ramirez-Sossa M.I. (1999). Robust stability of multivariate polynomials part 2: Polytopic coefficient variations. Multidimensional Systems and Signal Processing 10, 21–32
Kharitonov V.L., Zhabko A. (1994). Robust stability of time-delay Systems. IEEE Transactions on Automatic Control 39(12): 2388–2397
Ortiz-Moctezuma, B. (2005). Análisis de estabilidad robusta de quasipolynomios y polinomios multivariables. Ph.D. Dissertation, In Spanish, Cinvestav, México, September 2005.
Pontryagin L. (1995). On the zeros of some elementary trascendental functions, English Translation. American Mathematical Society Translation 2, 95–110
Rantzer A. (1992). Stability conditions for polytopes of polynomials. IEEE Transactions on Automatic Control 37(1): 79–89
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Torres-Muñoz, J.A., Kharitonov, V.L. & Ortiz-Moctezuma, M.B. Reduced stability testing set for a diamond-type family of quasipolynomials. Multidim Syst Sign Process 20, 25–37 (2009). https://doi.org/10.1007/s11045-008-0052-5
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DOI: https://doi.org/10.1007/s11045-008-0052-5