Non-fragile saturation control of nonlinear positive Markov jump systems with time-varying delays

This paper investigates non-fragile saturation control of nonlinear positive Markov jump systems, which contain sector nonlinear functions and time-varying delays. The saturation controller to be designed is supposed to have either multiplicative or additive gain uncertainty. First, a sufficient con...

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Bibliographic Details
Published in:Nonlinear dynamics 2019-07, Vol.97 (2), p.1495-1513
Main Authors: Zhang, Junfeng, Raïssi, Tarek, Li, Shicheng
Format: Article
Language:English
Subjects:
Automatic
Automotive Engineering
Classical Mechanics
Control
Control systems design
Dynamical Systems
Engineering
Engineering Sciences
Feedback control
Linear programming
Markov processes
Mechanical Engineering
Nonlinear control
Nonlinear systems
Optimization
Original Paper
Programmable logic devices
Saturation
State feedback
Vibration
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Summary:This paper investigates non-fragile saturation control of nonlinear positive Markov jump systems, which contain sector nonlinear functions and time-varying delays. The saturation controller to be designed is supposed to have either multiplicative or additive gain uncertainty. First, a sufficient condition for the positivity of an auxiliary nonlinear system with sector restriction is established. By employing a nonlinear co-positive-type Lyapunov functional, a non-fragile control of the considered systems with multiplicative and additive perturbations is proposed in terms of linear programming, respectively. A set of non-fragile state feedback controllers associated with auxiliary feedback gains is designed using a matrix decomposition technique. Based on the designed controllers, the corresponding closed-loop systems are positive and stable with an L 1 -gain performance and the system states converge to a cone set. Furthermore, an optimization method is developed to estimate the maximum invariant set. Compared with existing results, the proposed technique is not only less conservative but also reliable in practice. Finally, two simulation examples are provided to show the effectiveness of the obtained results.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-019-05068-5