A converse to the deterministic separation principle

Jochen Trumpf; Harry L. Trentelman

doi:10.1016/j.sysconle.2016.02.021

A converse to the deterministic separation principle

Jochen Trumpf^*, Harry L. Trentelman

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In the classical theory of finite-dimensional linear time-invariant systems in state space form the term deterministic separation principle refers to the observation that a stabilizing output feedback controller can be constructed by first constructing an asymptotic state observer that is then coupled to a stabilizing state feedback controller. In this paper we discuss the following converse problem: Can every stabilizing output feedback controller be realized as interconnection of an asymptotic state observer and a stabilizing state feedback controller? We will provide an affirmative answer to this question (modulo a number of technicalities) in a behavioral setting and with the help of rational representations.

Original language	English
Pages (from-to)	2-9
Number of pages	8
Journal	Systems and Control Letters
Volume	101
DOIs	https://doi.org/10.1016/j.sysconle.2016.02.021
Publication status	Published - 1 Mar 2017

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AU - Trumpf, Jochen

AU - Trentelman, Harry L.

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N2 - In the classical theory of finite-dimensional linear time-invariant systems in state space form the term deterministic separation principle refers to the observation that a stabilizing output feedback controller can be constructed by first constructing an asymptotic state observer that is then coupled to a stabilizing state feedback controller. In this paper we discuss the following converse problem: Can every stabilizing output feedback controller be realized as interconnection of an asymptotic state observer and a stabilizing state feedback controller? We will provide an affirmative answer to this question (modulo a number of technicalities) in a behavioral setting and with the help of rational representations.

AB - In the classical theory of finite-dimensional linear time-invariant systems in state space form the term deterministic separation principle refers to the observation that a stabilizing output feedback controller can be constructed by first constructing an asymptotic state observer that is then coupled to a stabilizing state feedback controller. In this paper we discuss the following converse problem: Can every stabilizing output feedback controller be realized as interconnection of an asymptotic state observer and a stabilizing state feedback controller? We will provide an affirmative answer to this question (modulo a number of technicalities) in a behavioral setting and with the help of rational representations.

KW - Behavioral approach

KW - Linear systems

KW - Output feedback

KW - Separation principle

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U2 - 10.1016/j.sysconle.2016.02.021

DO - 10.1016/j.sysconle.2016.02.021

M3 - Article

SN - 0167-6911

VL - 101

SP - 2

EP - 9

JO - Systems and Control Letters

JF - Systems and Control Letters

ER -

A converse to the deterministic separation principle

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