"LPV systems with stochastic parameters"
Corentin Briat
Division of Optimization and Systems Theory
Royal Institute of Technology (KTH)
Abstract
Quite recently, the approaches based on linear matrix inequalities (LMI)
have attracted more and more interest. Indeed, they extend prior
approaches based on Riccati equations/inequalities to a wider class of
systems, including LPV systems. The interest of LPV systems is mainly
due to their ability to approximate complex dynamical systems such as
nonlinear systems. Under the assumption that parameters are measured in
real-time, this framework allows for the design of gain-scheduled
controllers whose gains depend explicitly on the measured parameters.
Consequently, these controller are then able to stabilize a larger set
of systems than robust-controllers.
The objective of the talk is twofold. A first part will be devoted to an
introduction on LPV systems. How they are represented, which classes of
systems are embedded in the LPV systems class, how stability is studied,
what makes them more complex than LTI systems and, finally, how
stabilization can be performed. The second part will be devoted to the
introduction of a new class of LPV systems whose parameters evolve
accordingly to a Markov process. Such systems have not been studied in
the literature and seem to be of interest. It will be shown that
LMI-based necessary and sufficient conditions for stability and
stabilizability can be obtained.
SlidesBiographical Information
Corentin Briat received the MsC and PhD degree in Automatic Control from
the Grenoble Institute of Technology (Grenoble INP, former INPG) in
Grenoble, France in 2005 and 2008 respectively. In 2009, he was a
postdoc researcher on the delay-estimation in time-delay systems within
the ALIEN project, INRIA-Lille (France). Since September 2009, he is
working on the modeling, analysis and control of Internet congestion
control mechanisms in the ACCESS project at KTH (Stockholm, Sweden). His
main research interests include LPV/switched/jump systems, time-delay
systems and optimization.
http://www.briat.info
