发布时间：2018-09-25 | 来源：国科大雁栖湖校区教1-225
报告人：Ying Tan(The University of Melbourne, Australia)
An introduction of nonlinear systems
【Abstract】This lecture talked about an overview of nonlinear systems and highlighted that most engineering systems are nonlinear.
Linear Vs. Nonlinear
【Abstract】This lecture talked about some interesting phenomena that can be only observed from nonlinear systems.
Existence and uniqueness of solutions
【Abstract】This lecture provided some sufficient conditions to ensure the existence and uniqueness of solutions of nonlinear systems.
An introduction to Lyapunov stability
【Abstract】This lecture provided standard epsilon delta definitions of stability, attractivity and asymptotic stability for nonlinear time-invariant systems.
Lyapunov second method
【Abstract】This lecture provided sufficient conditions to guarantee stability properties of nonlinear time invariant systems using positive definite Lyapunov functions.
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.
Class K，K_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 |
【Abstract】This lecture provided the existence of Lyapunov functions when solutions of nonlinear systems have some stability properties.
【Abstract】This lecture provided some examples to show how to use Lyapunov techniques to show the stability properties of nonlinear systems.
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.
【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.