Computation of delay intervals for stability of time-delay systems

This paper addresses the problem of computing the delay intervals for stability of time-delay systems. Time-delays are frequently a source of instability and quite often difficult to estimate. The major features of the method are: (1) the delay uncertainty is represented by a relative error, i.e., h = h0(1 + δ); (2) the time-delay system is recast by a representation that is compatible with robust control analysis, which requires a norm-bounded modeling uncertainty and stable transfer function; and (3) a new tool, i.e., singular phase value, is proposed to find the exact bounds on the delay that sufficiently stabilize the time-delay system. The method can be used to find the first delay interval for stability but it can also be extended to find other delay intervals using standard robust control tools; therefore, the proposed method is suitable for computer implementation. With a simple modification, the proposed method can also be used to test the robust stability of various controller schemes under closed-loop conditions.