Modeling and control of a sorption process using 2D systems theory

Dymkov, M.; Gałkowski, Krzysztof; Rogers, Eric; Dymkou, Vitali; Dymkou, S.

doi:10.1109/nds.2011.6076869

Cited by 10 publications

(5 citation statements)

References 9 publications

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“…In this section, the filter design method is applied to an approximate model of gas absorption process which is represented by a 2D Roesser model. The following non-linear hyperbolic partial differential equation of second order is commonly used to model the processes of gas absorption, water stream heating and air drying [49,50]…”

Section: Simulation Examplementioning

confidence: 99%

filtering for discrete‐time 2D T–S fuzzy systems with finite frequency disturbances

Duan

Shen

Ghous³

et al. 2019

IET Control Theory & Applications

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Section: Simulation Examplementioning

confidence: 99%

filtering for discrete‐time 2D T–S fuzzy systems with finite frequency disturbances

Duan

Shen

Ghous³

et al. 2019

IET Control Theory & Applications

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“…In some application similar to sorption processes considered in Dymkov et al (2011) one or both independent variables are given on finite interval. If t 2 ≤ T 2 and t 1 is unbounded or t 1 ≤ T 1 and t 2 is unbounded it is reasonable to define stability by the following way Definition 3.…”

Section: Stability Of Nonlinear Continuous-time Roesser Type Systemsmentioning

confidence: 99%

“…One example of the former case is Dymkov et al (2011) where a 2D Roesser model was developed for a sorption process, which arises in waste water and sewage treatment. Conditions for a unique solution was also developed together with a representation formula.…”

Section: Introductionmentioning

confidence: 99%

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Stability analysis of 2D Roesser systems via vector Lyapunov functions

et al. 2017

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The paper gives new results that contribute to the development of a stability theory for 2D nonlinear discrete and differential systems described by a state-space model of the Roesser form using an extension of Lyapunov's method. One of the main difficulties in using such an approach is that the full derivative or its discrete counterpart along the trajectories cannot be obtained without explicitly finding the solution of the system under consideration. This has led to the use of a vector Lyapunov function and its divergence or its discrete counterpart along the system trajectories. Using this approach, new conditions for asymptotic stability are derived in terms of the properties of two vector Lyapunov functions. The properties of asymptotic stability in the horizontal and vertical dynamics, respectively, are introduced and analyzed. This new properties arise naturally for repetitive processes where one of the two independent variables is defined over a finite interval. Sufficient conditions for exponential stability in terms of the properties of one vector Lyapunov function are also given as a natural follow on from the asymptotic stability analysis.

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“…Example 3: Consider the following model of sorption process from industrial water supply and sewerage treatment industries (Dymkov, Galkowski, Rogers, Dymkou, & Dymkou, 2011). Let us consider the process with multiple subsystems, …”

Section: Remarkmentioning

confidence: 99%

H_∞control of a class of 2-D continuous switched delayed systems via state-dependent switching

Ghous

Xiang

2015

International Journal of Systems Science

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This paper addresses the problem of state feedback H ∞ stabilisation of 2-D (two-dimensional) continuous switched state delayed systems represented by the Roesser model using the multiple Lyapunov functional approach. First, an asymptotical stability condition of 2-D continuous switched systems with state-dependent switching is derived. Second, a sufficient condition for H ∞ performance of the underlying system is established. Third, a state feedback controller is proposed to ensure that the resulting closed-loop system has a prescribed H ∞ performance level under a state-dependent switching signal. All the results are developed in terms of linear matrix inequalities. Finally, three examples are provided to demonstrate the validity and effectiveness of the proposed method.

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Modeling and control of a sorption process using 2D systems theory

Cited by 10 publications

References 9 publications

filtering for discrete‐time 2D T–S fuzzy systems with finite frequency disturbances

filtering for discrete‐time 2D T–S fuzzy systems with finite frequency disturbances

Stability analysis of 2D Roesser systems via vector Lyapunov functions

H_∞control of a class of 2-D continuous switched delayed systems via state-dependent switching

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Modeling and control of a sorption process using 2D systems theory

Cited by 10 publications

References 9 publications

filtering for discrete‐time 2D T–S fuzzy systems with finite frequency disturbances

filtering for discrete‐time 2D T–S fuzzy systems with finite frequency disturbances

Stability analysis of 2D Roesser systems via vector Lyapunov functions

H∞control of a class of 2-D continuous switched delayed systems via state-dependent switching

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H_∞control of a class of 2-D continuous switched delayed systems via state-dependent switching