Using Lyapunov's direct method for wave suppression in reactive systems

Smagina, Yelena; Sheintuch, Moshe

doi:10.1016/j.sysconle.2005.12.001

Cited by 21 publications

(10 citation statements)

References 15 publications

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“…Partial differential equations model tremendous amount of processes: heat transfer, fluid dynamics, fusion reactions, wave propagation, etc. Such processes may require feedback control to remain stable, e.g., chemical reactors [1], oil drill strings [2], tokamaks [3], and rotating stall in axial compressors [4]. Here, we construct observers for 2D heat equations with continuous and sampled in time pointlike measurements.…”

Section: Introductionmentioning

confidence: 99%

Sampled-data H∞ filtering of a 2D heat equation under pointlike measurements

Selivanov

Fridman

2018

2018 IEEE Conference on Decision and Control (CDC)

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Section: Introductionmentioning

confidence: 99%

Sampled-data H∞ filtering of a 2D heat equation under pointlike measurements

Selivanov

Fridman

2018

2018 IEEE Conference on Decision and Control (CDC)

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“…To reduce the network workload an event-triggering mechanism (ETM) can be used. While there exists an extensive literature on event-triggered networked control of finite dimensional systems (see [34,37,28,22,7,15,42,31]), there are few works on eventtriggered control of diffusion PDEs, which are potentially of great interest in a long distance control of chemical reactors [33] or air polluted areas [24,4]. Eventtriggered control of distributed parameter systems was started in [39] via model reduction approach leading to local results concerning practical stability where no decay rate can be guaranteed for the initial system.…”

Section: Introductionmentioning

confidence: 99%

Distributed event-triggered control of diffusion semilinear PDEs

2016

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“…[1,2]. Networked control of distributed parameter systems may be applicable to long distance control of chemical reactors [3] or air polluted areas [4]. One of the main challenges in NCSs is a measurement sampling.…”

Section: Introductionmentioning

confidence: 99%

Sampled-data relay control of diffusion PDEs

Selivanov

Fridman

2017

Automatica

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We consider a vector reaction-advection-diffusion equation on a hypercube. The measurements are weighted averages of the state over different subdomains. These measurements are asynchronously sampled in time. Subject to matched disturbances, the discrete control signals are applied through shape functions and zero-order holds. The feature of this work is that we consider generalized relay control: the control signals take their values in a finite set. This allows for networked control through low capacity communication channels. First, we derive linear matrix inequalities (LMIs) whose feasibility guarantees the ultimate boundedness with a limit bound proportional to the sampling period. Then we construct a switching procedure for the controller parameters that ensures semi-global practical stability: for an arbitrarily large domain of initial conditions the trajectories converge to a set whose size does not depend on the domain size. For the disturbance-free system this procedure guarantees exponential convergence to the origin. The results are demonstrated by two examples: 2D catalytic slab and a chemical reactor.

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Using Lyapunov's direct method for wave suppression in reactive systems

Cited by 21 publications

References 15 publications

Sampled-data H∞ filtering of a 2D heat equation under pointlike measurements

Sampled-data H∞ filtering of a 2D heat equation under pointlike measurements

Distributed event-triggered control of diffusion semilinear PDEs

Sampled-data relay control of diffusion PDEs

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