On Delay-Independent Stability and Guaranteed Convergence Rate for Linear Time-Varying Continuous-Time Delay Systems

This work deals with linear continuous-time systems with delays, in the general case of time-varying matrices. We first consider the special case of positive systems of such class, introducing two different conditions of delay-independent global exponential stability formulated by means of linear inequalities. Moreover, guaranteed bounds on the exponential convergence rate are given as a function of the largest admissible delay. Then, employing a state-bounding approach built on the properties of positive systems, we extend the analysis to systems with no sign constraints. Due to the time-varying nature of the systems, all such conditions involve infinite-many tests. Hence, we discuss the significant special case of switching systems with delays, for which the conditions can be finitely tested.