Adaptive Observers for MIMO Discrete-Time LTI Systems

TL;DR

This paper introduces a novel adaptive observer for MIMO discrete-time LTI systems that guarantees bounded estimates regardless of excitation conditions, using RLS with covariance resetting.

Contribution

It presents a general adaptive observer design for MIMO LTI systems using RLS with covariance resetting, ensuring boundedness without excitation requirements.

Findings

Guarantees bounded estimates under all excitation conditions.

Demonstrates convergence and stability through detailed analysis.

Validates performance with simulation results.

Abstract

In this paper, an adaptive observer is proposed for multi-input multi-output (MIMO) discrete-time linear time-invariant (LTI) systems. Unlike existing MIMO adaptive observer designs, the proposed approach is applicable to LTI systems in their general form. Further, the proposed method uses recursive least square (RLS) with covariance resetting for adaptation that is shown to guarantee that the estimates are bounded, irrespective of any excitation condition, even in the presence of a vanishing perturbation term in the error used for updation in RLS. Detailed analysis for convergence and boundedness has been provided along with simulation results for illustrating the performance of the developed theory.