Robust Stabilization for Dynamic Systems with Multiple Time-Varying Delays and Nonlinear Uncertainties

2001 ◽  
Vol 108 (1) ◽  
pp. 155-174 ◽  
Author(s):  
J. H. Park
Keyword(s):  
Dynamic Systems ◽  
Robust Stabilization ◽  
Multiple Time ◽  
Time Varying ◽  
Nonlinear Uncertainties

Robust Decentralized Adaptive Control for Interconnected Systems With Time Delays

2005 ◽  
Vol 127 (4) ◽  
pp. 656-662 ◽  
Author(s):  
Changchun Hua ◽  
Xinping Guan ◽  
Peng Shi
Keyword(s):  
Time Delays ◽  
Large Scale ◽  
Robust Stabilization ◽  
Interconnected Systems ◽  
Multiple Time ◽  
Time Varying ◽  
Nonlinear Functions ◽  
Feedback Controllers ◽  
Large Scale Systems ◽  
Closed Loop Systems

The problem of robust stabilization for a class of time-varying nonlinear large-scale systems subject to multiple time-varying delays in the interconnections is considered. The interconnections satisfy the match condition, and are bounded by nonlinear functions that may contain a high-order polynomial with a time delay. Without the knowledge of these bounds, we present adaptive state feedback controllers that are continuous and independent of time delays. Based on the Lyapunov stability theorem, we prove that the controllers can render the closed loop systems uniformly ultimately bounded stable. We also apply the result to constructing adaptive feedback controllers to stabilize a class of interconnected systems whose nominal systems are linear. Finally, several examples are given to show the potential of the proposed techniques.

Adaptive Sliding Mode Tracking of Nonlinear Plants With Multiple Unknown Time-Varying State Delays

2008 ◽  
Author(s):  
Boris Mirkin ◽  
Per-Olof Gutman ◽  
Yuri Shtessel
Keyword(s):  
Dynamic Systems ◽  
Sliding Mode ◽  
External Disturbance ◽  
Nonlinear Dynamic Systems ◽  
Multiple Time ◽  
Time Varying ◽  
State Delays ◽  
Nonlinear Plants ◽  
Model Reference Adaptive ◽  
Mode Tracking

In this paper, we develop a sliding mode model reference adaptive control (MRAC) scheme for a class of nonlinear dynamic systems with multiple time-varying state delays which is robust with respect to unknown plant delays, to a nonlinear perturbation, and to an external disturbance with unknown bounds. An appropriate Lyapunov-Krasovskii type functional is introduced to design the adaptation algorithms, and to prove stability.

Robust Reliable Control for a Class of Uncertain Discrete-Time Systems with Multiple Time-Varying Delays

2012 ◽  
Vol 630 ◽  
pp. 396-401
Author(s):  
Chong Li
Keyword(s):  
Discrete Time ◽  
Controller Design ◽  
Design Method ◽  
Robust Stabilization ◽  
System Stability ◽  
Multiple Time ◽  
Reliable Control ◽  
Time Varying ◽  
Robust Reliable Control ◽  
Delay Dependent

The robust reliable control design problem of uncertain discrete-time control systems with multiple time-varying delays is addressed in this article. Uncertainty in system is assumed to satisfy the norm-bounded condition and the time-delay parameter is time-varying unstructured. Under the proposed concepts of exponentially robust stability and exponentially robust stabilization, the delay-dependent exponential stability condition for the robust reliable control system is derived and a new delay-dependent state feedback controller design method is provided. The relationship between system stability and time-delays is also studied. Simulation study shows the effectiveness and feasibility of the proposed controller design method.

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