Finite‐region stability and finite‐region boundedness for 2D Roesser models

Zhang, Guangchen; Wang, Weiqun

doi:10.1002/mma.3982

Cited by 18 publications

(10 citation statements)

References 25 publications

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“…First, we devise a state feedback controller K , which ensures the system x + ( i , j )=( A + B K ) x ( i , j ) FRS. According to theorem 3.3 in Zhang and Wang, let

c_{1}^{'} = 0.58

c_{2}^{'} = 0.07

, with

c_{1}^{'} + c_{2}^{'} < c_{1} = 0.7

, c ′ = c 2 =20, η =0.9, using LMI toolbox of Matlab, the conditions are feasible with

α_{1}^{'} = 1.05

α_{2}^{'} = 1.10

β_{1}^{'} = 35.5

β_{2}^{'} = 3.45

, and the state feedback controller is

K = false[0.3850, 0.2750 false] .

Next, we design an observer gain L to guarantee the system FRB. By using LMI control toolbox and Theorem , a feasible solution of the LMIs to and to with η =0.9, α 1 =1.05, α 2 =1.06 can be derived as follows

P = [\begin{matrix} 7.1720 & 0 \\ * & 105.5938 \end{matrix}], Q = [\begin{matrix} 22.2962 & 0 \\ * & 32.3899 \end{matrix}], M = [\begin{matrix} - 2.6483 \\ - 0.5877 \end{matrix}] .

Thus, we can obtain

L = Q^{- 1} M = ([], \begin{matrix} center \\ array - 0 \end{matrix})

…”

Section: Resultsmentioning

confidence: 99%

“…The definitions of FRS and FRB for 2‐D discrete systems given in Zhang and Wang are different from those of FTS and FTB for 1‐D systems. Thus, we slightly change the definitions of FRS and FRB for 2‐D systems, to keep their forms consistent with the definitions of FTS and FTB for 1‐D systems.…”

Section: Preliminaries and Problem Statementmentioning

confidence: 99%

“…First, we introduce the Luenberger observer of systems to :

ξ^{+} false(i, j false) = A ξ false(i, j false) + B u false(i, j false) + L ((), C ξ false(i, j false) - y false(i, j false)), ξ_{0} false(i, j false) = 0,

where

L = ([], \begin{matrix} center \\ array L_{1} \\ array L_{2} \end{matrix})

is the observer gain matrix with approximate dimensions. Now, we feedback the state estimation via the state feedback controller

u false(i, j false) = K ξ false(i, j false) .

Note that when the state feedback controller K exists, it can be designed by using the method given in theorem 3.3 of Zhang and Wang . Therefore, it is reasonable to make the following assumption.…”

Section: Preliminaries and Problem Statementmentioning

confidence: 99%

“…We first introduce a Luenberger observer with a state feedback controller, which is a special dynamic output feedback controller. Then we get a closed‐loop system that treats the state estimation errors as external perturbations, and the boundedness condition of the external perturbations can be guaranteed by theorem 3.1 in Zhang and Wang . In this way, the problem of finite‐region stabilization for discrete 2‐D Roesser models via dynamic output feedback is converted into the problem of designing an observer to guarantee the closed‐loop system finite‐region boundedness (FRB).…”

Section: Introductionmentioning

confidence: 99%

“…Then we get a closed-loop system that treats the state estimation errors as external perturbations, and the boundedness condition of the external perturbations can be guaranteed by theorem 3.1 in Zhang and Wang. 25 In this way, the problem of finite-region stabilization for discrete 2-D Roesser models via dynamic output feedback is converted into the problem of designing an observer to guarantee the closed-loop system finite-region boundedness (FRB). Furthermore, we give a generic sufficient condition and a sufficient condition that is solvable by linear matrix inequalities (LMIs) for the existence of such an dynamic output feedback controller that guarantees the closed-loop system to be FRS.…”

mentioning

confidence: 99%

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Finite‐region stabilization via dynamic output feedback for 2‐D Roesser models

Hua

Wang

et al. 2018

Math Methods in App Sciences

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Finite‐region stability (FRS), a generalization of finite‐time stability, has been used to analyze the transient behavior of discrete two‐dimensional (2‐D) systems. In this paper, we consider the problem of FRS for discrete 2‐D Roesser models via dynamic output feedback. First, a sufficient condition is given to design the dynamic output feedback controller with a state feedback‐observer structure, which ensures the closed‐loop system FRS. Then, this condition is reducible to a condition that is solvable by linear matrix inequalities. Finally, viable experimental results are demonstrated by an illustrative example.

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“…First, we devise a state feedback controller K , which ensures the system x + ( i , j )=( A + B K ) x ( i , j ) FRS. According to theorem 3.3 in Zhang and Wang, let

c_{1}^{'} = 0.58

c_{2}^{'} = 0.07

, with

c_{1}^{'} + c_{2}^{'} < c_{1} = 0.7

, c ′ = c 2 =20, η =0.9, using LMI toolbox of Matlab, the conditions are feasible with

α_{1}^{'} = 1.05

α_{2}^{'} = 1.10

β_{1}^{'} = 35.5

β_{2}^{'} = 3.45

, and the state feedback controller is

K = false[0.3850, 0.2750 false] .

P = [\begin{matrix} 7.1720 & 0 \\ * & 105.5938 \end{matrix}], Q = [\begin{matrix} 22.2962 & 0 \\ * & 32.3899 \end{matrix}], M = [\begin{matrix} - 2.6483 \\ - 0.5877 \end{matrix}] .

Thus, we can obtain

L = Q^{- 1} M = ([], \begin{matrix} center \\ array - 0 \end{matrix})

…”

Section: Resultsmentioning

confidence: 99%

Section: Preliminaries and Problem Statementmentioning

confidence: 99%

“…First, we introduce the Luenberger observer of systems to :

ξ^{+} false(i, j false) = A ξ false(i, j false) + B u false(i, j false) + L ((), C ξ false(i, j false) - y false(i, j false)), ξ_{0} false(i, j false) = 0,

where

L = ([], \begin{matrix} center \\ array L_{1} \\ array L_{2} \end{matrix})

is the observer gain matrix with approximate dimensions. Now, we feedback the state estimation via the state feedback controller

u false(i, j false) = K ξ false(i, j false) .

Section: Preliminaries and Problem Statementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Finite‐region stabilization via dynamic output feedback for 2‐D Roesser models

Hua

Wang

et al. 2018

Math Methods in App Sciences

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Exponential Stability and H∞$$ {H}_{\infty } $$ Controller Design for 2‐D Discrete‐State Systems in Roesser Model With Directional Delays

2024

Optim Control Appl Methods

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This study looks at the problems related to exponential stability and controller design for a specific class of two‐dimensional discrete‐state systems (2‐D‐DSS) with directional constant delays (DCDs) in the Roesser model. Initially, by applying the two‐dimensional (2‐D) Lyapunov–Kravoskii functional approach, a condition is formulated as a linear matrix inequality (LMI) to ensure that the system remains exponentially stable while achieving an performance level of . Following this, a approach for designing a state feedback controller (SFB‐) is presented as a practical application of the derived results. Finally, several examples are provided to demonstrate the effectiveness of the proposed results.

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