Robust stability and H∞ performance analysis of interval-dependent time delay systems

Robust stability and performance analysis techniques are presented for time-delay systems consisting of the feedback interconnection of a linear time-delay system, with a bounded and casual linear operator. This linear operator features all the parameter and/or dynamical uncertainties excluding the delay elements. The delays considered are non-commensurate, time-invariant but uncertain, residing within a bounded interval excluding zero. A (sufficient) delay-free comparison system is formed by replacing the delay elements with parameter-dependent filters, satisfying certain properties. It is shown that robust stability of this finite dimensional comparison system, guarantees stability of the original time-delay system. A (necessary) comparison system is also provided. It is shown that the worst case H_∞ performance of the sufficient (necessary) comparison system provides an upper (a lower) bound for the H_∞ performance of the time-delay system. An LMI formulation is given for calculating an upper bound for the worst-case H_∞ performance of the time-delay system.