Convergence within a polyhedron: controller design for time-delay systems with bounded disturbances

This study considers linear systems with state/input time-varying delays and bounded disturbances. The authors study a new problem of designing a static output feedback controller which guarantees that the state vector of the closed-loop system converges within a pre-specified polyhedron. Based on t...

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Bibliographic Details
Published in:IET control theory & applications Vol. 9; no. 6; pp. 905 - 914
Main Authors: Nam, Phan Thanh, Pathirana, Pubudu Nishantha, Trinh, Hieu
Format: Journal Article
Language:English
Published: The Institution of Engineering and Technology 13.04.2015
Subjects:
Algorithms
bounded disturbances
closed‐loop system
control system synthesis
Controllers
convergence
convex optimisation algorithms
convex programming
Delay
delay systems
Disturbances
feedback
free‐weighting matrices
free‐weighting matrix technique
linear matrix inequalities
linear systems
Lyapunov methods
Lyapunov‐Krasovskii method
Mathematical models
Output feedback
output feedback control matrix
Polyhedrons
prespecified polyhedron
Regular Papers
Search methods
search problems
state transformation
state vector
state/input time‐varying delays
static output feedback controller designing
time‐delay systems
time‐varying systems
two‐dimensional search method
vectors
time-varying systems
delay systems
convergence
prespecified polyhedron
two-dimensional search method
free-weighting matrix technique
state vector
state/input time-varying delays
feedback
linear matrix inequalities
Lyapunov-Krasovskii method
search problems
output feedback control matrix
control system synthesis
convex programming
linear systems
convex optimisation algorithms
free-weighting matrices
vectors
time-delay systems
static output feedback controller designing
bounded disturbances
state transformation
closed-loop system
Lyapunov methods
ISSN:1751-8644, 1751-8652
Online Access:Get full text
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Summary:This study considers linear systems with state/input time-varying delays and bounded disturbances. The authors study a new problem of designing a static output feedback controller which guarantees that the state vector of the closed-loop system converges within a pre-specified polyhedron. Based on the Lyapunov–Krasovskii method combining with the free-weighting matrix technique, a new sufficient condition for the existence of a static output feedback controller is derived. The author's condition is expressed in terms of linear matrix inequalities with two parameters need to be tuned and therefore can be efficiently solved by using a two-dimensional search method combining with convex optimisation algorithms. To be able to obtain directly an output feedback control matrix from the derived condition, they propose an appropriate combination between a state transformation with a choice of a special form of the free-weighting matrices. The feasibility and effectiveness of the derived results are illustrated through five numerical examples.
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ISSN:1751-8644
1751-8652
DOI:10.1049/iet-cta.2014.0628