Interval Observer Design for One Class of Uncertain Linear Strictly Metzlerian Time-Delay Systems

Dušan Krokavec,Anna Filasová,Mehmet Emir Koksal

doi:10.1155/2020/6667569

Dušan Krokavec, Anna Filasová + Show 1 more

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https://doi.org/10.1155/2020/6667569

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Abstract

The paper is concerned with design requirements when the problem of nonnegative state estimation for one class of uncertain linear Metzlerian time-delay systems with constant delays is tackled, while system states take nonnegative values whenever the initial conditions are nonnegative, the upper and lower system matrix bounds are strictly Metzler matrices, and the upper and lower output matrix bounds are nonnegative matrices. By defining positive definite diagonal matrix variables and introducing an associate structure of linear matrix inequalities, the design conditions are proven, guaranteeing if they are feasible, the resulting observer gain matrix is positive and the reflected observer system matrices are strictly Metzler and Hurwitz. A numerical example illustrates the solvability of the proposed design conditions.

Highlights

Positive systems often occur in modeling and control of the class of processes, whose state variables do not have physical meaning unless they are nonnegative [1, 2]
E main motivation of this paper is to present the design conditions based on strict linear matrix inequalities (LMIs), for interval observers related to one class of time-delayed uncertain
A novel approach is presented in the paper to address the problem of effectively computing a positive observer gain that establishes the set of stable strictly Metzler observer matrices in interval Metzlerian time-delay observer design

Summary

Introduction

Positive systems often occur in modeling and control of the class of processes, whose state variables do not have physical meaning unless they are nonnegative [1, 2]. Stability and stabilization of this class of systems are reported, e.g., in [3,4,5], and related methods, based on linear programming (LP) and linear matrix inequalities (LMIs), are considered for positive stabilization and observer design [6,7,8,9,10]. Admitting the equivalent relation between positive system asymptotic stability and diagonal square stability established in [11], and reflecting a large number of parametric constraints [12], a useful unification is an LMI-based design strategy for linear positive (Metzlerian) systems presented in [13]. A counterpart of this approach is outlined in [15] to provide, for given system matrix bounds, the system state estimation in projected intervals. Interval observer algorithms for uncertain Metzlerian systems, with LMI projection of given interval bounds, are analyzed in [20]

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