New Results for Robust Stability of Discrete Bilinear Uncertain Time-Delay Systems

In this paper, new results for the problem of the robust stability of discrete homogeneous bilinear time-delay systems subjected to nonlinear or parametric uncertainties are addressed. Applying a concise upper bound to the Lyapunov equation approach and then associating some linear algebraic techniques, several delay-independent conditions are presented to assure the robust stability of the aforementioned systems. One of the features of the present criteria is that they are independent of any Lyapunov equation, although the Lyapunov equation approach is adopted. Comparing to an existing work, it is shown that the obtained results are sharper. Finally, all obtained results are applied to solve the same problem of discrete bilinear uncertain systems and discrete time-delay systems with/without uncertainties. Concise criteria for the robust stability of the mentioned systems are developed, and comparisons between the obtained results and those appeared in the literature are also made. It is shown that all obtained results in this work are either tighter or more concise.