Robust L2-Gain Observation for structured uncertainties: An LMI approach

The robust L
2
-gain estimation is investigated for general uncertain systems with structured uncertainties. A new estimation structure is introduced: the Augmented-Gain Observer which encompasses both filters and observers and allows robust estimation even for some classes of unstable systems. Our approach is based on a separation of graphs theorem using frequency dependent Integral Quadratic Constraints. We prove that the design of an Augmented-Gain Observer ensuring a robust L
2
-gain performance can be expressed as a convex optimization problem. This problem involves Linear Matrix Inequalities constraints and can be solved using an efficient algorithm. A numerical example illustrates the interest of the method.