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

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.

Keywords

• Multiple-input-multiple-output (MIMO) systems
• linear time-varying (LTV) systems
• setmembership interval state estimator
• interval analysis
• discrete-time systems