Abstract
The paper considers the stability issue of linear systems with commensurate delays. This issue can be well characterised by the distribution of roots of system's characteristic equation. At first, distribution boundary of the roots (with positive real parts) is explicit given in a practical way. Subsequently, a reliable graphical stability criterion for calculating the number of unstable roots is deduced, associating with auxiliary polynomial which plays an important role in the analysis of high order and complex systems. Moreover, a procedure for drawing the winding curve of characteristic function in finite path is proposed. At last, typical examples are given to illustrate that the result carried out is reliable and efficient.
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