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**Stability of infinite dimensional interconnected systems with impulsive and stochastic disturbances.**
*(English)*
Zbl 1406.93081

Summary: Some research on the stability with mode constraint for a class of infinite dimensional look-ahead interconnected systems with impulsive and stochastic disturbances is studied by using the vector Lyapunov function approach. Intuitively, the stability with mode constraint is the property of damping disturbance propagation. Firstly, we derive a set of sufficient conditions to assure the stability with mode constraint for a class of general infinite dimensional look-ahead interconnected systems with impulsive and stochastic disturbances. The obtained conditions are less conservative than the existing ones. Secondly, the controller for a class of look-ahead vehicle following systems with the above uncertainties is constructed by the sliding mode control method. Based on the obtained new stability conditions, the domain of the control parameters of the systems is proposed. Finally, a numerical example with simulations is given to show the effectiveness and correctness of the obtained results.

### MSC:

93B12 | Variable structure systems |

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

93C73 | Perturbations in control/observation systems |

### Keywords:

infinite dimensional interconnected systems; stability; impulsive and stochastic disturbances; sliding mode control
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\textit{X. Xu} et al., Abstr. Appl. Anal. 2014, Article ID 471481, 14 p. (2014; Zbl 1406.93081)

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### References:

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