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Boundary Feedback Control of PDE-Systems: Stability Analysis with Lyapunov Functions
Held by Prof. Martin Gugat (Universität Erlangen-Nürnberg)
In many applications in control engineering, the problem to respond to disturbances of the system appears. Typically, the disturbance occurs at some unknown point that is far away from the point where sensing and actuation equipment is installed. It is an interesting challenge to develop good feedback control laws for such cases. We consider systems that can be modeled as 2x2 PDEs of hyperbolic type. To show the exponential stability of the system, we work with Lyapunov functions. The Lyapunov functions have to be chosen in such a way that a negative upper bound for their time-derivative that depends linearly on the Lyapunov function can be obtained from the system dynamics.