Interval State Estimator Design Using the Observability Matrix for Multiple Input Multiple Output Linear Time-Varying Discrete-Time Systems

Awais Khan,Wei Xie

doi:10.1109/access.2019.2954125

Abstract

In this paper, a novel numerical scheme to set-membership interval state estimator design is proposed for the multiple-input-multiple-output (MIMO) linear time-varying (LTV) discrete-time systems using systems observability matrix and its past input/output values. The proposed method is more simple and efficient. First, an interval state estimator is designed that will generate a tight interval vector for the real state vector in a guaranteed way by employing interval analysis and consistency techniques for the single-input-single-output (SISO) systems. The proposed interval state estimator technique is then extended easily to the MIMO systems. Secondly, the estimation errors dynamics bounds are computed a-priori to measurements for the unknown but bounded uncertainties. Finally, the convergence of the width of the interval state vector towards a known value in finite time is provided to prove the boundedness of the interval state vector and estimation error that further quantify the accuracy of the developed technique. The performance and comparison with already existing techniques are highlighted through numerical examples.

Highlights

The unknown system states estimation is one of the most challenging and fundamental problem in many engineering fields, for instance, to design control laws or faults detection, all the state variables of the system must be available for measurements, and observers have the ability to estimate the unknown state variables efficiently [1]–[4]
The only difference between the set-membership interval state estimator design proposed for the SISO systems compared to the MIMO systems is the computation of the inverse
The design of set-membership interval state estimator based on observability matrix for the SISO and MIMO linear timevarying discrete-time systems is investigated in this paper

Summary

INTRODUCTION

The unknown system states estimation is one of the most challenging and fundamental problem in many engineering fields, for instance, to design control laws or faults detection, all the state variables of the system must be available for measurements, and observers have the ability to estimate the unknown state variables efficiently [1]–[4]. It is not always possible to find an observer gain such that the estimation error dynamics are nonnegative and stable To overcome this restriction, many techniques have been proposed based on coordinates transformation [17], [26]–[28]. A novel set-membership interval state estimator design is proposed based on the observability matrix for MIMO linear time-varying discrete-time systems. The finite-time convergence of the width of the estimated state vector towards a known value is provided, which significantly improves the accuracy of the proposed technique It shows that our technique is similar to the standard interval observers approach in the sense of stability analysis.

NOTATIONS

MIMO SYSTEM

INTERVAL PREDICTOR

1) COMPARATIVE SIMULATION RESULTS

EXAMPLE 2

CONCLUSION