This chapter presents an extension and offers a more comprehensive overview of our previous paper entitled “Stability conditions for a class of nonlinear time delay systems” published in “Nonlinear Dynamics and Systems Theory” journal. We first introduce a more complete approach of the nonlinear system stability for the single delay case. Then, we show the application of the obtained results to delayed Lur’e Postnikov systems. A state space representation of the class of system under consideration is used and a new transformation is carried out to represent the system, with delay, by an arrow form matrix. Taking advantage of this representation and applying the Kotelyanski lemma in combination with properties of M-matrices, some new sufficient stability conditions are determined. Finally, illustrative example is provided to show the easiness of using the given stability conditions.
Part of the book: Nonlinear Systems