An LMI condition for robust stability of polynomial matrix polytopes.

*(English)*Zbl 0982.93057The authors propose a new sufficient condition for robust stability of polynomial matrix polytopes. They combine two results obtained previously for less complex problems, namely a stability test for polynomial matrices expressed in the form of the LMI feasibility problem and a robust stability condition for constant matrix polytopes [see J. C. Geromel, M. C. de Oliveira and L. Hsu, LMI characterization of structural and robust stability, Linear Algebra Appl. 285, 69-80 (1998; Zbl 0949.93064)] based on the idea of an extra degree of freedom introduced by an additional arbitrary matrix enabling linear dependence of the condition in the parameters. This in turn leads to reduction of conservatism inherent to the quadratic stability conditions. The stability regions considered in the paper include the left half plane and the unit disk so that the obtained condition may be used to check robust stability of both continuous-time and discrete-time multivariable systems. The authors also present the results of their numerical experiments in which they used the LMI control toolbox of MATLAB. The results prove the reduction of the conservatism inherent to the quadratic stability tests.

Reviewer: A.Šwierniak (Gliwice)

##### MSC:

93D09 | Robust stability |

93C73 | Perturbations in control/observation systems |

15A39 | Linear inequalities of matrices |

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\textit{D. Henrion} et al., Automatica 37, No. 3, 461--468 (2001; Zbl 0982.93057)

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##### References:

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