Robust state estimation for uncertain nonlinear systems described using integral quadratic constraints: an LMI formulation

Considers estimating the states of a physical system represented as a linear time-invariant (LTI) system with uncertainties and nonlinearities Δ represented in the form of a linear fractional transformation (LFT). The description used for Δ were in the form of several integral quadratic constraints (IQCs). This problem is a nontrivial generalization of a Kalman filter and an H_∞ filter to include uncertainties and nonlinearities. While it is known that this problem can be written as a convex optimization problem using a “S-procedure losslessness theorem”, the main contribution of this work is to show that it can be written as a linear matrix inequality as well. An important consequence is the following interesting physical interpretation: the optimal robust H_∞ filter is such that the worst case sensor noise is the one that makes the output measurements zero. This interpretation was known to be true for the standard H_∞ filter in the absence of uncertainties and nonlinearities