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

Abstract

Considers estimating the states of a physical system represented as a linear time-invariant (LTI) system with uncertainties and nonlinearities /spl Delta/ represented in the form of a linear fractional transformation (LFT). The description used for /spl Delta/ were in the form of several integral quadratic constraints (IQCs). This problem is a nontrivial generalization of a Kalman filter and an H/sub /spl infin// 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/sub /spl infin// 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/sub /spl infin// filter in the absence of uncertainties and nonlinearities.