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Ellipsoidal set-theoretic approach for stability of linear state-space models with interval uncertainty

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  • Qiu, Zhiping
  • Müller, Peter C.
  • Frommer, Andreas

Abstract

This paper addresses the issue of conservatism in the stability robustness bound obtained by the Lyapunov matrix equation solution. Ellipsoidal set-theoretical approach is employed to improve the bound on the interval uncertainty of an asymptotically stable linear system for robust stability. The formula of determination of the ellipsoid from the given interval uncertainties is given in this paper. The improved bound is obtained, using ellipsoidal set-theoretical approach, on vector uncertainties (i.e. structured uncertainty) as well as on a matrix uncertainties (i.e. unstructured uncertainty). The bound is shown to be less conservative than that obtained by the interval set-theoretical approach. Examples given include comparison of the ellipsoidal set-theoretical approach with the interval set-theoretical approach.

Suggested Citation

  • Qiu, Zhiping & Müller, Peter C. & Frommer, Andreas, 2001. "Ellipsoidal set-theoretic approach for stability of linear state-space models with interval uncertainty," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 57(1), pages 45-59.
    • Handle: RePEc:eee:matcom:v:57:y:2001:i:1:p:45-59
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    Cited by:

    1. Qiu, Zhiping & Lin, Qiang & Wang, Xiaojun, 2008. "Convex models and probabilistic approach of nonlinear fatigue failure," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 129-137.
    2. Tavazoei, Mohammad Saleh & Haeri, Mohammad, 2009. "A note on the stability of fractional order systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1566-1576.

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