New results on stability and L ∞ ‐gain analysis for positive linear differential‐algebraic equations with unbounded time‐varying delays

Summary This article addresses the problems of stability and L ∞ ‐gain analysis for positive linear differential‐algebraic equations with unbounded time‐varying delays for the first time. First, we consider the stability problem of a class of positive linear differential‐algebraic equations with unbounded time‐varying delays. A new method, which is based on the upper bounding of the state vector by a decreasing function, is presented to analyze the stability of the system. Then, by investigating the monotonicity of state trajectory, the L ∞ ‐gain for differential‐algebraic systems with unbounded time‐varying delay is characterized. It is shown that the L ∞ ‐gain for differential‐algebraic systems with unbounded time‐varying delay is also independent of the delays and fully determined by the system matrices. Two numerical examples are given to illustrate the obtained results.