# Weekly Activities

New results on stability and $L_ {\infty}$-gain analysis for positive linear differential-algebraic equations with unbounded time-varying delays
 Speaker: Nguyen Huu SauTime: 9h, Friday, April 11, 2019 Location: Room 513, Building A6, Institute of MathematicsAbstract: This paper addresses the problems of stability and $L_ {infty}$ gain analysis for positive linear differential-algebraic equations with unbounded time-varying delays. 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 $L_ {infty}$ -gain for differential-algebraic systems with unbounded time-varying delay is characterized. It is shown that the $L_ {infty}$-gain for differential-algebraic systems with unbounded time-varying delay is also independent of the delays and fully determined by the system matrices. A numerical example is given to illustrate the obtained results

### Highlights

 12/04/21, Conference:CIMPA School “Functional Equations: Theory, Practice and Interactions” 22/04/21, Conference:Hội thảo TỐI ƯU VÀ TÍNH TOÁN KHOA HỌC lần thứ 19 29/06/21, Conference:The 7th International Conference on Random Dynamical Systems