# 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

 20/09/19, Colloquium Lecture:Some inverse source problems in semilinear fractional PDEs 27/09/19, Conference:Hội thảo Hình học-Giải tích 11/10/19, Conference:Hội thảo "Giải tự do và các bất biến đối đồng điều" 11/11/19, Conference:The IMH School Introduction to Algebraic Schemes and Cohomology 04/12/19, Conference:Hội nghị Đại số-Lý thuyết số-Hình học và Tô pô 2019