Seminar Details
2006-02-21 (14.00 pm) : "Estimation and enlargement of domains of attraction"
At Euler building
Organized by Mathematical Engineering
Speaker :
Bazanella, Alexandre
Abstract :
Establishing that an asymptotically stable equilibrium has a sufficiently large domain of attraction (DOA)
is crucial for its stability to have practical meaning. Hence, providing such sufficiently large DOA's is also
a major control objective to be pursued. In nonlinear systems theory, estimation of DOA's and control
design are most usually tackled by means of Lyapunov's direct method. The estimates of DOA's obtained
by means of Lyapunov analysis depend strongly on the particular Lyapunov function used and can be very
poor, which also diminishes its value as a control design tool in this context. In this seminar I will present
a numerical method, based on LMI's, to determine Lyapunov functions for rational nonlinear systems.
On the other hand, most Lyapunov based control design theory has been concerned with the achievement
of global asymptotic stability, which is sometimes impossible and most often unnecessary. I'll present some
results on LgV control and the more general interconnection and damping assignment (IDA) control design
method, concerning the enlargment of DOA's of open-loop stable equilibria. I will also present a dynamic
feedback scheme which inherits these properties and usually results in better performance than LgV and IDA
. Finally, applications to the real-time assessment and the enhancement of electric power systems security
will be presented.