LMI-Based Reset Unknown Input Observer for State Estimation of Linear Uncertain Systems

TL;DR

This paper introduces a Reset Unknown Input Observer (R-UIO) for linear systems that uses reset laws and LMI techniques to improve transient response and estimation accuracy in the presence of disturbances.

Contribution

It presents a novel R-UIO design applying reset theory within an LMI framework, enhancing transient response and stability for both SISO and MIMO systems.

Findings

Significant reduction in estimation error norm.

Improved transient response demonstrated through simulations.

Applicable to both SISO and MIMO systems.

Abstract

This paper proposes a novel kind of Unknown Input Observer (UIO) called Reset Unknown Input Observer (R-UIO) for state estimation of linear systems in the presence of disturbance using Linear Matrix Inequality (LMI) techniques. In R-UIO, the states of the observer are reset to the after-reset value based on an appropriate reset law in order to decrease the $L_2$ norm and settling time of estimation error. It is shown that the application of the reset theory to the UIOs in the LTI framework can significantly improve the transient response of the observer. Moreover, the devised approach can be applied to both SISO and MIMO systems. Furthermore, the stability and convergence analysis of the devised R-UIO is addressed. Finally, the efficiency of the proposed method is demonstrated by simulation results.