On the Convergence to Zero of Infinite Products of Interval Matrices

A necessary and sufficient condition for the consecutive powers of an interval matrix to converge to the null matrix was established by Mayer. Motivated by the issue of globally asymptotic stability of Takagi--Sugeno free fuzzy systems with time-varying uncertainty, we study the conditions for the infinite products of a finite number of interval matrices to converge to the null matrix. As an application, convergence to null matrix of infinite products of the associated finite interval matrices implies the globally asymptotic stability of Takagi--Sugeno free fuzzy systems with time-varying uncertainty.

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