Seminar Details
2009-03-10 (14.00) : An LMI approach for uncertain nonlinear systems
At Euler building
Organized by Mathematical Engineering
Speaker :
Daniel COUTINHO (Pontifícia Universidade Católica do Rio Grande do Sul, Brazil.)
Abstract :
In the last two decades, LMI-based techniques have been successfully applied to cope with uncertain linear
systems in a wide diversity of applications such as robustness analysis, control and filter design, H2 and H-infinity design,
control saturation and state-delayed systems. Together with the evolution of available LMI solvers, in terms of reliability,
computational burden and easily of coding, many researchers have developed different LMI methodologies to deal with
nonlinear systems. Recently, several different LMI-based techniques have been derived for nonlinear systems. One can
divide these works in two main classes: (i) the linear-like representations, and (ii) the SOS (sum of squares) approach.
The linear-like representations preserve the system state space representation and thus they can be applied for synthesis purposes.
However, global stability conditions are of difficult handling. In contrast, the SOS-based approaches may handle global stability
conditions but they are not suitable to control design. In this talk, the Differential-Algebraic Representation (DAR) framework is
introduced to deal with a large class of nonlinear systems. Some recent results on stability analysis, performance and control
synthesis are presented and a discussion is carried out on the advantages and shortcomings of the approach.