A Sufficient Condition of Robust Stabilization of Interval Plants with Compensators

It has been shown that a first-order linear compensator stabilizes an interval plant with numerator and denominator being Kharitonov polynomials if and only if sixteen extreme plants are Hurwitz. The sixteen extreme plants are generated by using the four extreme polynomials of the numerator and the four extreme polynomials of the denominator corresponding to the maximum or minimum values of real or imaginary parts of the polynomials. In this paper we provide a sufficient condition that for any given compensator if the derivative of the argument of the compensator with respect to frequency is zero or negative then it is necessary and sufficient to check the sixteen extreme plants for the closed-loop stability. Although only the sufficient condition is given here, many special forms of compensator satisfy the condition that the spin velocity of the Kharitonov rectangle is zero or negative. For example, if all the compensator poles are negative and all the compensator zeros are positive, it is enough to check the sixteen extreme plants for the Hurwitz stability of the closed-loop polynomial.