# Low-order control design for LMI problems using alternating projection methods

@article{Grigoriadis1996LoworderCD,
title={Low-order control design for LMI problems using alternating projection methods},
author={Karolos M. Grigoriadis and Robert E. Skelton},
journal={Automatica},
year={1996},
volume={32},
pages={1117-1125}
}
Computational techniques based on alternating projections are proposed to solve control design problems described by linear matrix inequalities (LMIs). In particular, we concentrate on the stabilization and the suboptimal H, output feedback control design problems. These problems can be described by a pair of LMIs and an additional coupling condition. This coupling condition is convex for the full-order control design problem, but convexity is lost for the control problem of order strictly less… CONTINUE READING
Highly Cited
This paper has 200 citations. REVIEW CITATIONS

#### Citations

##### Publications citing this paper.
Showing 1-10 of 124 extracted citations

## Noniterative ${\cal H}_{\infty }$-Based Model Order Reduction of LTI Systems Using LMIs

IEEE Transactions on Control Systems Technology • 2009
View 11 Excerpts
Highly Influenced

## A Reduction in Conservatism for Convex Linear-Quadratic Simultaneous Performance Design

Peter Dorato, Chaouki T. AbdallahDepartment
2007
View 5 Excerpts
Highly Influenced

## Reliability and Efficiency of Extended Linearization Algorithms for General Robust Control Problems

View 7 Excerpts
Highly Influenced

## Stability analysis of discrete singular fuzzy systems

Fuzzy Sets and Systems • 2005
View 4 Excerpts
Highly Influenced

## Robust Static Output-Feedback Control for Uncertain Linear Discrete-Time Systems via the Generalized KYP Lemma ?

View 3 Excerpts
Highly Influenced

## On design of low order H-infinity controllers

View 3 Excerpts
Highly Influenced

## Design of a Control System using Linear Matrix Inequalities for the Active Vibration Control of a Plate

View 2 Excerpts
Highly Influenced

## A Newton-like method for solving rank constrained linear matrix inequalities

2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601) • 2004
View 4 Excerpts
Highly Influenced

## Reduced-order H/sub /spl infin// and L/sub 2/-L/sub /spl infin// filtering via linear matrix inequalities

IEEE Transactions on Aerospace and Electronic Systems • 1997
View 4 Excerpts
Highly Influenced

## A Hybrid Design Approach for Output Feedback Exponential Stabilization of Markovian Jump Systems

IEEE Transactions on Automatic Control • 2018
View 1 Excerpt

#### 201 Citations

Citations per Year
Semantic Scholar estimates that this publication has 201 citations based on the available data.

See our FAQ for additional information.

#### References

##### Publications referenced by this paper.
Showing 1-10 of 28 references

## Parametrization of all stabilizing controllers via quadratic Lyapunov functions

T. Iwasaki, R. E. Skelton
J. Optim. Theory Applies, 83,291-307. • 1995
View 5 Excerpts
Highly Influenced

## Linear Matrix Inequalities In System And Control Theory

Proceedings of the IEEE • 1998
View 6 Excerpts
Highly Influenced

## Rank minimization under LMI constraints: a framework for output feedback problems

L. El Ghaoui, P. Gahinet
Proc. European Control. Co& Groningen, pp. 1176-1179. • 1993
View 5 Excerpts
Highly Influenced

## Method of Successive Projections for Finding a Common Point of Sets in Metric Spaces

View 5 Excerpts
Highly Influenced

## Proximity maps for convex sets

W. Cheney, A. A. Goldstein
Proc. Am. Math. Sot., 12,448-450. • 1959
View 6 Excerpts
Highly Influenced

## Linear Controller Design : Limits of Performance

View 3 Excerpts
Highly Influenced

## A primal-dual potential reduction method for problems involving matrix inequalities

Math. Program. • 1995

## All controllers for the general H∞ control problem: LMI existence conditions and state space formulas

Automatica • 1994
View 5 Excerpts

## Interior-Point Polynomial Algorithms in Convex Programming (Y. Nesterov and A. Nemirovskii)

SIAM Review • 1994
View 1 Excerpt

## Alternating convex projection methods for discrete-time covariance control design

Grigoriadis. K.M., R. E. Skelton, A. E. Frazho
Proc. 32nd IEEE Conf on Decision and Control, San Antonio, TX, pp. 1782-1786. • 1993
View 1 Excerpt