New algebraic criteria for absolute stability of nonlinear systems

In this paper, new and simple algebraic criteria are derived via elementary proofs to provide easy sufficient conditions for the standard absolute stability problems of nonlinear systems, i.e. Lur'e problems. These criteria are equivalent to the famous graphical circle criteria and Popov criterion. By means of the Sturm theorem and the Euclidean division algorithm, a Routh‐Hurwitz‐like Sturm criterion is obtained. No graphical technique is needed. Only basic numerical manipulations are involved in the new criteria.