DOI: 10.3724/SP.J.1004.2013.02150

Acta Automatica Sinica (自动化学报) 2013/39:12 PP.2150-2153

Stability Criteria of Linear Time-delay Systems with Dependent Delays

This paper reveals that only fewer of the linear time-delay (LTD) systems with dependent delays (LTD-DD systems) can satisfy the stability condition for linear time-delay systems with independent delays (LTD-ID systems), since there is a strict limitation for the parameters of the LTD-DD systems. The characteristic polynomials of LTD-DD systems belong to quasipolynomials, and the roots of the quasipolynomials are the function of the multiple delays, which make the stability test of LTD-DD systems di±cult. To solve the problem, based on 2-D hy-brid polynomials, some stability criteria of LTD-DD systems are proposed. Examples show that the proposed stability criteria are simple and valid, and that the proposed theorem can solve the conservatism problem of existing LMI stability testing algorithms.

Key words:Control theory, time-delay systems, quasipolynomials, two-dimensional polynomials, stability criteria

ReleaseDate:2014-07-21 17:04:32

Funds:National Natural Science Foundation of China (60572093) and National Defence Project (102476)