H∞-Control for Linear Time-Delay Systems with Markovian Jumping Parameters

2000 ◽  
Vol 105 (1) ◽  
pp. 73-95 ◽  
Author(s):  
K. Benjelloun ◽  
E. K. Boukas ◽  
O. L. V. Costa
Keyword(s):  
Time Delay ◽  
Linear Time ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Markovian Jumping Parameters ◽  
Markovian Jumping

Robust Stabilizability of Uncertain Linear Time-Delay Systems With Markovian Jumping Parameters

1996 ◽  
Vol 118 (4) ◽  
pp. 776-783 ◽  
Author(s):  
K. Benjelloun ◽  
E. K. Boukas ◽  
H. Yang
Keyword(s):  
Time Delay ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Markovian Jumping Parameters ◽  
Markovian Jumping ◽  
Linear Type ◽  
Continuous State ◽  
The Stability

In this paper, we deal with the robust stabilizability of the class of uncertain linear time-delay systems with Markovian jumping parameters and unknown but bounded uncertainties. Under the assumption of the complete access to the continuous state, the stochastic controllability of the nominal system and the boundedness of the system’s uncertainties, sufficient conditions which guarantee the robustness of the stability of this class of systems are given. The control law which guarantees the robustness of the stabilizability is linear-type or saturation-type. An example is presented to illustrate the usefulness of the proposed theoretical results.

scholarly journals Stochastic stability of linear time-delay system with Markovian jumping parameters

1997 ◽  
Vol 3 (3) ◽  
pp. 187-201 ◽  
Author(s):  
K. Benjelloun ◽  
E. K. Boukas
Keyword(s):  
Time Delay ◽  
Stochastic Stability ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Delay System ◽  
Delay Systems ◽  
Necessary Condition ◽  
Markovian Jumping Parameters ◽  
Markovian Jumping ◽  
The Stability

This paper deals with the class of linear time-delay systems with Markovian jumping parameters (LTDSMJP). We mainly extend the stability results of the deterministic class of linear systems with time-delay to this class of systems. A delay-independent necessary condition and sufficient conditions for checking the stochastic stability are established. A sufficient condition is also given. Some numerical examples are provided to show the usefulness of the proposed theoretical results.

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