Delay-dependent H ∞ Control for Uncertain 2-D Discrete Systems with State Delay in the Roesser Model

Xu, Jian‐Xin; Nan, Yurong; Zhang, Guijun; Liu, Ou; Ni, Hongjie

doi:10.1007/s00034-012-9507-x

Cited by 20 publications

(7 citation statements)

References 9 publications

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“…Consequently, from [13,27], we have lim i+ j→∞ E{|x i, j | 2 } = 0, which implies from Definition 1 that the system (1) is asymptotically stable.…”

Section: Into (18) Leads Tomentioning

confidence: 88%

“…As we all know, the thermal process of a heat exchanger can be expressed in the following partial differential equation [16,27]:…”

Section: Numerical Examplementioning

confidence: 99%

“…Similar to the technique used in [16,27], it is easy to verify that (42) can be converted into the form of 2-D Roesser model with Markovian jump parameters matrices:…”

Section: Numerical Examplementioning

confidence: 99%

See 2 more Smart Citations

Delay-Dependent Stability and $$H_{\infty }$$ H ∞ Control for 2-D Markovian Jump Delay Systems with Missing Measurements and Sensor Nonlinearities

Dai

Guo

2016

Circuits Syst Signal Process

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This paper investigates the problem of stability and H ∞ control for 2-D time-delayed Markovian jump systems with missing measurements and sensor nonlinearities. The measured signals transmitted between the system and the controller are supposed to be imperfect, which involves missing measurements and sensor nonlinearities. The data missing is described by a random variable that obeys the Bernoulli binary distribution, and the sensor nonlinearities are assumed to satisfy the sector conditions. The problem addressed is the design of an output feedback controller such that the resulting closed-loop system is mean-square asymptotically stable and has a prescribed H ∞ performance level. By using the Lyapunov method and the discrete Jensen inequality, stability criteria and H ∞ performance level are established, and then, the controller design problem is cast into optimization problems via two methods. Finally, a numerical example is exploited to illustrate the effectiveness of the proposed design method.

show abstract

“…Consequently, from [13,27], we have lim i+ j→∞ E{|x i, j | 2 } = 0, which implies from Definition 1 that the system (1) is asymptotically stable.…”

Section: Into (18) Leads Tomentioning

confidence: 88%

“…As we all know, the thermal process of a heat exchanger can be expressed in the following partial differential equation [16,27]:…”

Section: Numerical Examplementioning

confidence: 99%

See 1 more Smart Citation

Delay-Dependent Stability and $$H_{\infty }$$ H ∞ Control for 2-D Markovian Jump Delay Systems with Missing Measurements and Sensor Nonlinearities

Dai

Guo

2016

Circuits Syst Signal Process

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show abstract

“…By utilizing the free-weighting matrix technique, delay-dependent robust stability conditions were derived in [40] for a class of 2-D systems described by the second FM model with delays and uncertainties. In [10,18,38], the problems of H ∞ control and filtering design for discrete-time 2-D systems with time-delay and disturbances were studied by using the Lyapunov-Krasovskii functional (LKF) method combining with Jensen-based inequality and free-weighting matrix technique.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of two-dimensional Markovian jump state-delayed systems in the Roesser model with uncertain transition probabilities

Hien

Trinh

2016

Information Sciences

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“…Hien and Trinh [18] investigated the problems of designing positive observers for 2D Roesser systems and the stability and stabilisation of Markov jump systems described by the Roesser model [19]. A series of

H_{\infty}

control problems of Roesser system have been investigated in [20–22].…”

Section: Introductionmentioning

confidence: 99%

Quasi‐convex combination method and its application to the stability analysis of 2D discrete‐time Roesser systems with time‐varying delays

Huang

et al. 2018

IET Control Theory & Applications

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Delay-dependent H ∞ Control for Uncertain 2-D Discrete Systems with State Delay in the Roesser Model

Cited by 20 publications

References 9 publications

Delay-Dependent Stability and $$H_{\infty }$$ H ∞ Control for 2-D Markovian Jump Delay Systems with Missing Measurements and Sensor Nonlinearities

Delay-Dependent Stability and $$H_{\infty }$$ H ∞ Control for 2-D Markovian Jump Delay Systems with Missing Measurements and Sensor Nonlinearities

Stability analysis of two-dimensional Markovian jump state-delayed systems in the Roesser model with uncertain transition probabilities

Quasi‐convex combination method and its application to the stability analysis of 2D discrete‐time Roesser systems with time‐varying delays

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