Discrete-Time PI-Nonlinear ${cal H}_{\\infty }$ Estimation

Author

Aliyu, M.D.S. ; Boukas, El-Kebir ; Chinniah, Yuvin

Author_Institution

Dept. of Mech. Eng., Ecole Polytech. de Montreal, Montreal, QC, Canada

Volume

55

Issue

3

fYear

2010

fDate

3/1/2010 12:00:00 AM

Firstpage

784

Lastpage

790

Abstract

In this technical note, exact and approximate solutions of the discrete-time suboptimal proportional-integral-H _∞-estimation problem for affine nonlinear systems using finite-dimensional estimators (filters) are presented. Sufficient conditions for the solvability of the problem are given in terms of discrete-time Hamilton-Jacobi-Isaac´s equations. For linear systems, it is shown that, these equations reduce to a system of linear-matrix inequalities. Simulation results are also presented to show the benefit of the new approach.

Keywords

H^∞ control; Jacobian matrices; PI control; differential equations; discrete time systems; linear matrix inequalities; linear systems; multidimensional systems; nonlinear systems; suboptimal control; affine nonlinear system; discrete time Hamilton-Jacobi-Isaac equation; discrete time PI nonlinear H_∞ estimation; finite dimensional estimator; linear matrix inequality; linear systems; suboptimal PI-H_∞ estimation; ${cal L}_{2}$-gain; Hamilton-Jacobi-Isaacs equations (HJIEs); discrete-time nonlinear ${cal H}_{infty }$ estimation; linear-matrix inequalities (LMIs); proportional-integral (PI)-estimators;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2010.2040501

Filename

5406046

Discrete-Time PI-Nonlinear Estimation

Aliyu, M.D.S. ; Boukas, El-Kebir ; Chinniah, Yuvin

jour

Discrete-Time PI-Nonlinear ${cal H}_{\\infty }$ Estimation