Sliding Mode Control of One-Sided Lipschitz Nonlinear Markovian Jump Systems With Partially Unknown Transition Rates

Li, Yuan; Sun, Qingdong; Ren, Junchao; Liu, Yang

doi:10.1109/access.2020.3020323

Cited by 4 publications

(4 citation statements)

References 36 publications

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“…From (38), it can be seen that (14) is reduced to (36), by pre-and post-multiplying(14) with −1 and . Therefore, the closed-loop system (5) is stochastically stable.…”

Section: Resultsmentioning

confidence: 99%

Stochastic Stabilization for Discrete-Time Markovian Jump Systems With Time-Varying Delay and Two Markov Chains Under Partly Known Transition Probabilities

Liu

et al. 2021

IEEE Access

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This paper investigates the problem of state feedback controller design for discrete-time Markovian jump systems(MJSs) with time delay and two Markov chains under partly known transition probabilities. First, by constructing improved Lyapunov-Krasovskii functional(LKF), utilizing the properties that the sum of each row is one in a transition probability matrix and some tractable linear matrix inequalities(LMI), a sufficient condition is established such that the system under consideration is stochastically stable. Second, the design method of time-delay-dependent state feedback controller is proposed to ensure that the resulting closed-loop system is stochastically stable. Since no free matrix variables are applied under the proposed conditions, the method proposed reduce the complexity of calculations. Finally, two simulation examples are presented to show the effectiveness of the proposed method. Compared with the existing literature, in the proposed method not only the conservatism is reduced under the derived stability and stabilization conditions, but also the total number of matrix inequalities is less.

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“…From (38), it can be seen that (14) is reduced to (36), by pre-and post-multiplying(14) with −1 and . Therefore, the closed-loop system (5) is stochastically stable.…”

Section: Resultsmentioning

confidence: 99%

Stochastic Stabilization for Discrete-Time Markovian Jump Systems With Time-Varying Delay and Two Markov Chains Under Partly Known Transition Probabilities

Liu

et al. 2021

IEEE Access

Self Cite

View full text Add to dashboard Cite

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“…Remark 5: Theorem 1 is valid even if W (0) > 0, which implies system (1)- (2) and observer ( 7)-( 10) do not need to have identical initial conditions. In the case where W (0) = 0, by applying ( 31)- (32), the L 2 gain (instead of the RMS gain) from ξ to e f would be bounded by ν.…”

Section: A Observer Designmentioning

confidence: 99%

“…Thus the set of systems that are both OSL and QIB would be equivalent to the set of TL systems. The constant associated with the TL condition is however always positive, while the constants for the OSL and QIB conditions are generally smaller than the TL constant for the same system, and can also be positive, negative, or even zero [32], [33]. Therefore, these two conditions could reduce conservativeness when designing observers using linear matrix inequalities (LMIs) [34].…”

Section: Introductionmentioning

confidence: 99%

A Nonlinear Observer for Robust Fault Reconstruction in One-Sided Lipschitz and Quadratically Inner-Bounded Nonlinear Descriptor Systems

et al. 2021

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This article introduces a nonlinear observer to reconstruct faults in a class of nonlinear descriptor systems affected by disturbances, in both the state and output equations. The fault enters the system through nonlinear functions in both its state and output equations. The original system is first transformed such that design freedom in its structure is easier to exploit, and then a nonlinear observer is designed based on the transformed system to reconstruct the fault. Linear matrix inequalities are used to determine the gains of the observer such that the effect of the disturbances on the fault reconstruction is bounded. Finally, three simulation examples are carried out to verify the effectiveness of the scheme.

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“…Descriptor systems theory is an essential branch of modern control theory [1,6]. Meanwhile, Markovian jump systems (MJSs) are a special kind of multimodal stochastic hybrid system, and the modes can switch from one to another at different times [7,8]. Descriptor Markovian jump systems (DMJSs) can be modeled when descriptor systems experience sudden changes such as environmental mutation, component failures, and changes in subsystem interconnection.…”

Section: Introductionmentioning

confidence: 99%

Lower Triangular Factor-Based Fault Estimation and Fault-Tolerant Control for Descriptor Markovian Jump Systems with Multiple Faults

Shi

Bao

2022

Symmetry

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This paper considers the observer-based fault estimation and fault-tolerant control for descriptor Markovian jump systems (DMJSs). The goal of this paper is to estimate the actuator faults, sensor faults, and the state simultaneously, and then design a controller based on the estimation to stabilize the DMJS. Firstly, the state, actuator faults, and sensor faults are extended to new state variables to obtain an augmented system. Then, a lower triangular factor-based estimation observer (LTFEO) is proposed to estimate the state and multiple faults and to eliminate the influence of sensor faults. It is proved that the descriptor error system is derivative input-to-state stable (DISS) with respect to the derivative of the faults. Furthermore, based on the fault estimation, a fault-tolerant control scheme is proposed to guarantee the overall closed-loop system DISS. Finally, a numerical example is given to verify the effectiveness of the proposed estimation scheme and control strategy.

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Sliding Mode Control of One-Sided Lipschitz Nonlinear Markovian Jump Systems With Partially Unknown Transition Rates

Cited by 4 publications

References 36 publications

Stochastic Stabilization for Discrete-Time Markovian Jump Systems With Time-Varying Delay and Two Markov Chains Under Partly Known Transition Probabilities

Stochastic Stabilization for Discrete-Time Markovian Jump Systems With Time-Varying Delay and Two Markov Chains Under Partly Known Transition Probabilities

A Nonlinear Observer for Robust Fault Reconstruction in One-Sided Lipschitz and Quadratically Inner-Bounded Nonlinear Descriptor Systems

Lower Triangular Factor-Based Fault Estimation and Fault-Tolerant Control for Descriptor Markovian Jump Systems with Multiple Faults

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