Distribution of roots of quasi-polynomials of neutral type

Speaker: Qing-Long Han，Swinburne University of Technology

Inviter: 系统所

Title: Distribution of roots of quasi-polynomials of neutral type

Language: English

Time & Venue: 2026.01.07   09：00-11：00  N205

Abstract: In this invited talk, we first introduce several criteria that are proposed for the distribution of roots of quasi-polynomials of neutral type with complex coefficients. Quasi-polynomials with complex coefficients play an important role in applications, such as consensus of multi-agent systems with a directed network topology. Compared with Pontryagin’s results, the derived criteria can be numerically implemented because the interval of the frequency for analyzing the behavior of the quasi-polynomial can be determined. Then we provide some Hurwitz stability criteria to judge whether all the roots of the quasi-polynomials are in the open left-half complex plane. These Hurwitz stability criteria can be employed to analyze the stability of linear time-invariant systems with commensurate delays. On the one hand, the criteria derived are general since quasi-polynomials of retarded type and quasi-polynomials with real coefficients are their special cases. On the other hand, the conditions in Hurwitz stability criteria are all necessary and sufficient. As a special case, we present several criteria for the distribution of roots of the quasi-polynomials with real coefficients. Finally, we apply the proposed criteria to consensus protocol design of multi-agent systems multi-agent systems using delayed state information.