EE Seminar: New stability and exact observability conditions for hyperbolic systems via LMIs

~~Speaker: Maria Terushkin,
M.Sc. student under the supervision of Prof. Emilia Fridman

Wednesday, January 27, 2016 at 15:00
Room 011, Kitot Bldg., Faculty of Engineering

New stability and exact observability conditions for hyperbolic systems via LMIs

Abstract
Lyapunov-based solutions of various control problems for finite-dimensional systems can be formulated in the form of Linear Matrix Inequalities (LMIs). The LMI approach to distributed parameter systems is capable of utilizing nonlinearities and of providing the desired system performance. For 1-D wave and beam equations different control problems were solved in terms of LMIs. However, there have not been yet extensions of such results to n-D hyperbolic equations.
The problem of estimating the initial state of 1-D wave equations with globally Lipschitz nonlinearities from boundary measurements on a finite interval was solved by using the sequence of forward and backward observers, and deriving the upper bound for exact observability time in terms of LMIs. In the present study, we generalize this result to n-D wave and plate equations on a unit hypercube. This extension includes new LMI-based exponential stability conditions that are based on n-D extensions of Poincare inequality and of the Sobolev inequality with tight constants.
 The presented simple finite-dimensional LMI conditions complete the theoretical qualitative results for exact observability of linear systems in a Hilbert space.