Finite-time dissipative control for singular discrete-time Markovian jump systems with actuator saturation and partly unknown transition rates

Ma, Yuechao; Jia, Xiaorui; Liu, Deyou

doi:10.1016/j.apm.2017.07.035

Cited by 84 publications

(47 citation statements)

References 45 publications

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“…Example This example deals with the problem of water quality in streams of some river. For this issue, a discretized water pollution model with multiple operating points is constructed . The model depicts, at time k , concentrations per unit volume of biological oxygen demand and dissolved oxygen, respectively.…”

Section: Numerical Examplesmentioning

confidence: 99%

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Robust H_∞ guaranteed cost control for discrete‐time switched singular systems with time‐varying delay

Regaieg

Kchaou

Chaabane

2018

Optim Control Appl Methods

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Summary This paper investigates the problem of control design for a class of uncertain switched singular systems with time‐varying delay. Under mode‐dependent average dwell time and using an appropriate Lyapunov‐Krasovskii functional, the exponential admissibility of the system is analyzed. In order to obtain less conservative conditions, the delay partitioning technique is adopted as well as the improved reciprocally convex approach. By means of the developed admissibility condition, a static output feedback controller is then designed using linear matrix inequality approach. Moreover, by solving an optimization convex problem with constraints, the switched controller is developed to ensure simultaneously the stability of the closed‐loop system and satisfy an optimized upper bound of both the linear quadratic guaranteed cost and the H∞ norm. Numerical examples are proposed to verify the efficiency and the merits of the method proposed.

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Section: Numerical Examplesmentioning

confidence: 99%

“…For this issue, a discretized water pollution model with multiple operating points is constructed. 54 The model depicts, at time k, concentrations per unit volume of biological oxygen demand and dissolved oxygen, respectively. The difference of concentrations are denoted by the state vector x(k) .…”

Section: Numerical Examplesmentioning

confidence: 99%

Robust H_∞ guaranteed cost control for discrete‐time switched singular systems with time‐varying delay

Regaieg

Kchaou

Chaabane

2018

Optim Control Appl Methods

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“…Defining the augmented system variable as ( ) = [ ( ) ( )] and using conditions (10) and (11), we have…”

Section: State Reachable Set Estimationmentioning

confidence: 99%

“…When singular systems experience abrupt changes in their structures, it is natural to model them as singular Markovian jump systems [1,2]. The analysis and synthesis of such class of systems have gained considerable attention because of their importance in applications (see, e.g., the literature [3][4][5][6][7][8][9][10] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Estimation and Synthesis of Reachable Set for Singular Markovian Jump Systems

Ding

Liu

2018

Complexity

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The problems of reachable set estimation and state-feedback controller design are investigated for singular Markovian jump systems with bounded input disturbances. Based on the Lyapunov approach, several new sufficient conditions on state reachable set and output reachable set are derived to ensure the existence of ellipsoids that bound the system states and output, respectively. Moreover, a state-feedback controller is also designed based on the estimated reachable set. The derived sufficient conditions are expressed in terms of linear matrix inequalities. The effectiveness of the proposed results is illustrated by numerical examples.

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“…It is worth mentioning that, in stochastic dynamical systems control design, a controller must be sought to stabilize the system, and it is always required to ensure satisfactory some performances. H ∞ control, passive control, dissipative control, and guaranteed cost control emerge at a historic moment. In many cases, it is impossible or high cost to obtain the transition probability exactly.…”

Section: Introductionmentioning

confidence: 99%

Integrated fault estimation and fault‐tolerant control for uncertain time‐varying delay nonlinear Markovian jump systems

2018

Intl J Robust & Nonlinear

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Summary This paper investigates the issues of fault estimation and fault‐tolerant control for a class of uncertain time‐varying delay nonlinear Markovian jump systems with simultaneous actuator and sensor faults. Firstly, by analyzing and reformulating the original system, a Markovian robust sliding‐mode observer is introduced to provide simultaneous estimations of the state and faults. Secondly, a novel stochastic integral sliding surface function is designed, and the sufficient criteria is derived in terms of linear matrix inequalities, which guarantees that the sliding‐mode dynamics and error system are asymptotically stable with definite appointed H∞ performance disturbance attenuation level. Then, a robust sliding‐mode control law scheme is sought to ensure the reachability of the sliding surface in a finite time interval. Finally, the effectiveness of the proposed methodology is verified by numerical and practical examples.

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Finite-time dissipative control for singular discrete-time Markovian jump systems with actuator saturation and partly unknown transition rates

Cited by 84 publications

References 45 publications

Robust H_∞ guaranteed cost control for discrete‐time switched singular systems with time‐varying delay

Robust H_∞ guaranteed cost control for discrete‐time switched singular systems with time‐varying delay

Estimation and Synthesis of Reachable Set for Singular Markovian Jump Systems

Integrated fault estimation and fault‐tolerant control for uncertain time‐varying delay nonlinear Markovian jump systems

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Finite-time dissipative control for singular discrete-time Markovian jump systems with actuator saturation and partly unknown transition rates

Cited by 84 publications

References 45 publications

Robust H∞ guaranteed cost control for discrete‐time switched singular systems with time‐varying delay

Robust H∞ guaranteed cost control for discrete‐time switched singular systems with time‐varying delay

Estimation and Synthesis of Reachable Set for Singular Markovian Jump Systems

Integrated fault estimation and fault‐tolerant control for uncertain time‐varying delay nonlinear Markovian jump systems

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Product

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Robust H_∞ guaranteed cost control for discrete‐time switched singular systems with time‐varying delay

Robust H_∞ guaranteed cost control for discrete‐time switched singular systems with time‐varying delay