Interval Raus criterion for stability analysis of linear systems with dependent coefficients in the characteristic polynomial

This paper addresses the stability analysis of linear continuous systems under interval uncertainties. An interval generalization of the known Raus criterion is suggested to estimate the stability of the system considered. It is based on obtaining the interval extensions of the elements of the Raus matrix which are nonlinear functions of independent system parameters. The case when these elements are independent intervals is considered. The interval extensions are also determined by using modified affine arithmetic. Two sufficient conditions on stability and instability of the linear system considered are obtained. A numerical example illustrating the applicability of the method suggested is solved at the end of the paper.