Robust stability of interval polynomials and matrices for linear systems

This paper addresses on the robust stability problem of interval polynomials and matrices of the continuous-time linear system (C-TLS) and discrete-time linear system (D-TLS) that contain the real uncertain parameters. The robust stability of the interval polynomials and matrices can be determined by three different robust stability criterions that check the global minimum of each order Hurwitz determinant or check the global minimum of each element in first column of Routh array. The linear matrix inequality (LMI) methods and parameters dependent Lyapunov functions (PDLF) methods are often used to effectively determine the robust stability of the interval matrices and polynomials, and in this paper, these robust criterions are also effective to determine the stability of the interval matrices and polynomials. The robust stability of the interval matrices can be transformed into the stability of an interval polynomial too. The third robust criterion can reduce the number of the optimization objectives, and as well as the computational complexity when determining the robust stability of the interval polynomials and matrices. Through applying the bilinear transformation, the three robust criterions can be extended into the interval polynomials and matrices of discrete-time linear system. Different examples of interval polynomials and matrices are studied to show the effectiveness and accurateness of the robust stability checking methods