Robust stability evaluation for discrete-time interval systems based on characteristic roots area

The physical parameters of controlled systems are uncertain and are accompanied by nonlinearity. The transfer function and the characteristic polynomial should, therefore, be expressed by interval (polytopic) polynomials, regardless of whether the input-output signals are continuous or discrete in time. This paper evaluates the robust stability of discrete-time control systems based on the existing area of characteristic roots (i.e., eigenvalues) on a z-plane. By applying a division algorithm to a set of the four corners of segment polynomials, a sufficient condition for the roots area, which is enclosed by a specified (circular) contour in a unit circle, is given. As a result, the discrimination of the roots area by finite calculations becomes possible. The above result corresponds to the sectorial D-stability of continuous-time control systems.