Delay‐dependent stability and stabilisation of two‐dimensional positive Markov jump systems with delays

Hien, Le Van; Trinh, Hieu

doi:10.1049/iet-cta.2016.1358

Cited by 27 publications

References 48 publications

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Event‐triggered control of nonlinear positive semi‐Markovian jump systems with randomly occurring actuator faults

Zhang

Cai

et al. 2020

Optim Control Appl Methods

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This article is concerned with the event‐triggered nonfragile reliable control of nonlinear positive semi‐Markovian jump systems with randomly occurring faults. The randomly occurring actuator fault, describing the phenomenon of the actuator fault appearing in a random way, is assumed to obey a semi‐Markovian process different from the jump process of the systems. The nonlinear function is located in a sector. Using a stochastic copositive Lyapunov function integrated with linear programming, an event‐triggered control strategy is employed to deal with the stochastic stabilization of the underlying systems, where the transition rates satisfy a polytopic uncertain condition. Nonfragile reliable controllers with additive and multiplicative perturbations are proposed for the considered systems, respectively. Compared with existing results, the obtained approach establishes a more general fault description and proposes a more practicable control design. Finally, the novelties of the proposed approach are verified via two examples.

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Event‐triggered control of nonlinear positive semi‐Markovian jump systems with randomly occurring actuator faults

Zhang

Cai

et al. 2020

Optim Control Appl Methods

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Stability analysis and saturation control for nonlinear positive Markovian jump systems with randomly occurring actuator faults

Zhang

Yang

Raïssi

2020

Intl J Robust & Nonlinear

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SummaryThis article investigates the stability analysis and control design of a class of nonlinear positive Markovian jump systems with randomly occurring actuator faults and saturation. It is assumed that the actuator faults of each subsystem are varying and governed by a Markovian process. The nonlinear term is located in a sector. First, sufficient conditions for stochastic stability of the underlying systems are established using a stochastic copositive Lyapunov function. Then, a family of reliable L1‐gain controller is proposed for nonlinear positive Markovian jump systems with actuator faults and saturation in terms of a matrix decomposition technique. Under the designed controllers, the closed‐loop systems are positive and stochastically stable with an L1‐gain performance. An optimization method is presented to estimate the maximum domain of attraction. Furthermore, the obtained results are developed for general Markovian jump systems. Finally, numerical examples are given to illustrate the effectiveness of the proposed techniques.

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Input–output gain analysis of positive periodic systems

Zhu

Lam

Ebihara

2021

Intl J Robust & Nonlinear

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This paper investigates the input‐output gains, including ℓ1‐ and ℓ∞‐gains and L1‐ and L∞‐gains, of discrete‐time and continuous‐time positive periodic systems. For the discrete‐time case, the input–output gain can be characterized by linear inequalities. For the continuous‐time case, the input–output gain characterization problem turns into the existence problem of a positive periodic vector function. Based on some necessary and sufficient input–output gain conditions, we find the ℓ1‐ (L1‐) gain of discrete‐time (continuous‐time) positive periodic systems is equivalent to the of ℓ∞‐ (L∞‐) gain of the associated dual systems. Finally, two numerical examples are given to illustrate the results.

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Delay‐dependent stability and stabilisation of two‐dimensional positive Markov jump systems with delays

Cited by 27 publications

References 48 publications

Event‐triggered control of nonlinear positive semi‐Markovian jump systems with randomly occurring actuator faults

Event‐triggered control of nonlinear positive semi‐Markovian jump systems with randomly occurring actuator faults

Stability analysis and saturation control for nonlinear positive Markovian jump systems with randomly occurring actuator faults

Input–output gain analysis of positive periodic systems

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