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[2018.7.17-7.18] 数学与系统科学青年精英学术活动季
举办时间:2018.7.17-7.18    地点:国科大雁栖湖校区教1-225

为增进国内外优秀青年科研人才与系统科学研究所的相互了解与学术合作,系统科学研究所将于2018年6—8月举办为期一个季度的“数学与系统科学青年精英学术活动季”。活动期间,将邀请20位左右近年获得博士学位的系统科学相关领域优秀青年学者来访,并作短课程和学术报告。以下是短课程、学术报告和报告人的相关信息:

报告人:Ying Tan(The University of Melbourne, Australia)

地点:国科大雁栖湖校区教1-225

      

2018.7.16 8:30-9:20

An introduction of nonlinear systems

【Abstract】This lecture talked about an overview of nonlinear systems and highlighted that most engineering systems are nonlinear.

 

2018.7.16 9:30-10:20

Linear Vs. Nonlinear

【Abstract】This lecture talked about some interesting phenomena that can be only observed from nonlinear systems.

 

2018.7.16 10:30-11:20

Existence and uniqueness of solutions

【Abstract】This lecture provided some sufficient conditions to ensure the existence and uniqueness of solutions of nonlinear systems.

 

2018.7.16 11:30-12:20

An introduction to Lyapunov stability

【Abstract】This lecture provided standard epsilon delta definitions of stability, attractivity and asymptotic stability for nonlinear time-invariant systems.

 

2018.7.17 8:30-9:20

Lyapunov second method

【Abstract】This lecture provided sufficient conditions to guarantee stability properties of nonlinear time invariant systems using positive definite Lyapunov functions.

 

2018.7.17 9:30-10:20

Linear systems and LaSalle invariance principle

【Abstract】This lecture provided necessary and sufficient conditions to ensure the stability properties of linear time invariant systems using Lyapunov equation. Moreover, LaSalle invariant principle was introduced to conclude attractivity of nonlinear systems when the derivative of a positive definite Lyapunov function is negative semi-definite.

 

2018.7.16 10:30-11:20

Class KK_inf and KL functions

【Abstract】This lecture introduced classes of nonlinear functions that can be used to capture positive definite Lyapunov functions and global asymptotic stable nonlinear systems. Some useful properties were introduced as well.

 

 2018.7.17 11:30-12:20

Nonlinear time varying systems

【Abstract】This lecture talked about uniform stability, uniform attractivity and uniform asymptotic stability of nonlinear time varying systems. Sufficient conditions using Lyapunov functions were provided.

 

 2018.7.18 8:30-9:20

Converse theorem

【Abstract】This lecture provided the existence of Lyapunov functions when solutions of nonlinear systems have some stability properties.

 

2018.7.18 9:30-10:20

examples

【Abstract】This lecture provided some examples to show how to use Lyapunov techniques to show the stability properties of nonlinear systems.

 

2018.7.18 10:30-11:20

LaSalle invariance principle

【Abstract】This lecture revisited the well-known LaSalle invariance principle for nonlinear time invariant systems. It also provided extensions to time varying systems and switched systems.

 

李迪章(明新科技大学,台湾)

2018.7.18 11:30-12:20

Matrosov Theorem

【Abstract】This lecture motivated the need of switched systems from engineers’ perspective. Moreover, the solutions of nonlinear time varying switched systems were discussed in terms of existence and uniqueness.

 

 

 

 

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