Delay-independent conditions of exponential ISS for linear time-varying delay differential systems

This work focuses on linear continuous-time systems with time-varying delays, in the general case of time-varying matrices. Initially, we explore the case of positive systems within this class and introduce two distinct delay-independent conditions of exponential input-to-state stability. Moreover, we provide guaranteed exponential convergence rates for such conditions, explicitly stating the ISS gains. Then, we extend our analysis to systems without sign constraints, adopting a state-bounding approach that takes advantage of the properties of positive systems. Due to the time-varying nature of the systems, all proposed conditions are in terms of an infinite number of inequalities. Hence, implementation issues are discussed and significant special cases in which the conditions can be cast into a linear programming problem of finite dimension are presented.