Delay-dependent robust stability and H/sub ∞/ control of jump linear systems with time-delay

2002 ◽  
Author(s):  
E.K. Boukas ◽  
G.X. Liu
Keyword(s):  
Time Delay ◽  
Linear Systems ◽  
Robust Stability ◽  
Jump Linear Systems ◽  
Delay Dependent

Robust Stability and H∞ Control of Discrete-Time Jump Linear Systems With Time-Delay: An LMI Approach*

2003 ◽  
Vol 125 (2) ◽  
pp. 271-277 ◽  
Author(s):  
E. K. Boukas and ◽  
Z. K. Liu
Keyword(s):  
Time Delay ◽  
Linear Systems ◽  
Robust Stability ◽  
Discrete Time ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Markov Jump ◽  
Jump Linear Systems ◽  
Markov Jump System ◽  
System With Time Delay

This paper considers the class of discrete-time jump linear systems with time-delay and polytopic uncertain parameters. The problems of delay-independent robust stability, stabilization and H∞ control are cast into the framework of linear matrix inequality (LMI) and thus solved by LMI Toolbox of Matlab. By extending the system state, the system with time-delay is converted into a higher dimension Markov jump system without time-delay, and thus can be handled as a standard jump linear system with uncertain parameters. Numerical examples are provided to show the usefulness of the theoretical results.

Measures of Robustness for Uncertain Time-Delay Linear Systems

1995 ◽  
Vol 117 (4) ◽  
pp. 633-635 ◽  
Author(s):  
Said Oucheriah
Keyword(s):  
Time Delay ◽  
Linear Systems ◽  
Robust Stability ◽  
Salient Feature ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Lyapunov Matrix ◽  
The Stability ◽  
Uncertain Time ◽  
Delay Dependent

Several delay-dependent criteria to test the stability of time-delay systems that were proposed require solving the Lyapunov matrix equation. This can be a troublesome task and often nontrivial. In this note, a delay-dependent sufficient condition that guarantees the robust stability of linear uncertain time-delay systems is presented. The stability test criterion derived in this paper is based on induced norms and matrix measures. The salient feature of the result obtained is its simplicity and ease in testing the robust stability of uncertain time-delay linear systems.

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