The regulator equations for regular linear systems

Vivek Natarajan, David S. Gilliam, George Weiss

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We investigate the state feedback regulator problem for exponentially stable plants belonging to the class of regular linear systems. The plant is driven by a linear completely unstable exosystem via a disturbance signal. The exosystem also generates the reference signal for the plant output. The state feedback regulator problem is to design a controller that has access to the states of the exosystem and the plant and which, while guaranteeing the stability of the closed-loop system without the exosystem, drives the tracking error to zero. We show that, under suitable assumptions, this problem is solvable if and only if a pair of algebraic equations, called the regulator equations, is solvable. We present an example that illustrates our theory.

Original languageEnglish
Title of host publication19th IFAC World Congress IFAC 2014, Proceedings
EditorsEdward Boje, Xiaohua Xia
PublisherIFAC Secretariat
Number of pages6
ISBN (Electronic)9783902823625
StatePublished - 2014
Event19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014 - Cape Town, South Africa
Duration: 24 Aug 201429 Aug 2014

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
ISSN (Print)1474-6670


Conference19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014
Country/TerritorySouth Africa
CityCape Town


  • Exosystem
  • Regular linear system
  • Regulator equations
  • State feedback regulator problem


Dive into the research topics of 'The regulator equations for regular linear systems'. Together they form a unique fingerprint.

Cite this