Kharitonov-like rectangle for the sectorial area stability

The physical parameters of control systems are uncertain and are accompanied by nonlinearity. The state space equation and the characteristic polynomial of the control system should, therefore, be expressed by an interval set of parameters. This paper examines the robust stability of that type of control system based on the characteristic roots which exist in a sectorial area on the left half s-plane. A sufficient condition for the robust stability is given by applying a division algorithm (Sturm's theorem) to the four corner polynomials, that is, a Kharitonov-like rectangle which covers all extreme points of the polytopic polynomial.