• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.205-212
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• 2014

This paper investigates mean square exponential dissipativity of singularly perturbed stochastic delay differential equations. The L-operator delay differential inequality and stochastic analysis technique are used to establish sufficient conditions ensuring the mean square exponential dissipativity of singularly perturbed stochastic delay differential equations for sufficiently small ${\varepsilon}$ > 0. An example is presented to illustrate the efficiency of the obtained results.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.135-140
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• 1998

The concept of dissipativity and passivity are of interest to us from a theoretical as well as a practical point of view. It is well known that the Riccati equation is derived from the dissipation inequality which expresses the fact that the system is dissipative; the energy stored inside the system doesn't exceed the amount of supply which flows into the system. The pencil model is regarded as a representation based on behavioral approach introduced by J.C. Willems. It has first order in the internal variable and zeroth order in the external variable. In general, any matrix pencil is transformed into a canonical form which is consist of several kind of sub-pencils, One of them has row full rank for $^\forall S\;\in\;\mathds{C}\;\bigcup{\infty}$, we call it under-determined mode of the model. In our opinion, most important properties of dynamical system lay in the mode. According to the properties of canonical form for pencil, it is shown that the storage function which characterizes the dissipativity of the system can be written as a LMI for the under-determined mode, if the system doesn't include impulse mode.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.64 no.11
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• pp.1598-1604
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• 2015

In this paper, we treat the problem of a robust finite-time dissipative state feedback controller design method for discrete-time singular systems with polytopic uncertainties. A BRL(bounded real lemma) for finite-time stability of discrete-time singular systems is derived. A finite-time dissipative state feedback controller design method satisfying finite-time stability and dissipativity is proposed by LMI(linear matrix inequality) technique on the basis of the obtained BRL. Moreover it is shown that the obtained condition can be extended into polytopic uncertain systems by proper manipulations. Finally, illustrative examples are given to show the applicability of the proposed method.

• Wind and Structures
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• v.22 no.1
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• pp.107-131
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• 2016

The need for a more affordable, reliable, clean and secure energy has led to explorations in non-traditional sources, particularly renewable energies. Wind is one of the cleanest energy sources that plays a significant role in augmenting sustainability. Wind turbines, as energy convertors, are usually tall and slender structures, and depending on their location (inland or offshore), they can be subject to high wind and/or strong wave loadings. These loads can cause severe vibrations with detrimental effects on energy production, structural lifecycle and initial cost. A dissipativity analysis study was carried out to know whether wind turbine towers require damping enhancement or rigidity modifications for vibration suppression. The results suggest that wind turbines are lightly damped structures and damping enhancement is a potential solution for vibration lessening. Accordingly, the paper investigates different damping enhancement techniques for vibration mitigation. The efficacy of tuned mass damper (TMD), tuned liquid column damper (TLCD), tuned sloshing damper (TSD), and viscous damper (VD) to reduce vibrations is investigated. A comparison among these devices, in terms of robustness and effectiveness, is conducted. The VD can reduce both displacement and acceleration responses of the tower, better than other types of dampers, for the same control effort, followed by TMD, TSD, and finally TLCD. Nevertheless, the use of VDs raises concerns about where they should be located in the structure, and their application may require additional design considerations.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.521-535
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• 2023

In this work, some various types of Dissipativity in random dynamical systems are introduced and studied: point, compact, local, bounded and weak. Moreover, the notion of random Levinson center for compactly dissipative random dynamical systems presented and prove some essential results related with this notion.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.63 no.7
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• pp.994-1000
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• 2014

This paper considers the problem of continuous and discrete time dissipative filter design method for the singular systems with polytopic uncertainties. Two bounded real lemmas (BRL) for the robust filters of dissipative singular systems along with the polytopic uncertainties are proposed on the basis of Lyapunov criterion. The sufficient conditions for both continuous and discrete time dissipative filter design methods are derived using the obtained BRL by linear matrix inequality (LMI) approach. Finally, the validities of the proposed methods are shown by numerical examples.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.457-478
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• 2014

In this paper, a 3D autonomous system, which has only stable or non-hyperbolic equilibria but still generates chaos, is presented. This system is topologically non-equivalent to the original Lorenz system and all Lorenz-type systems. This motivates us to further study some of its dynamical behaviors, such as the local stability of equilibrium points, the Lyapunov exponent, the dissipativity, the chaotic waveform in time domain, the continuous frequency spectrum, the Poincar$\acute{e}$ map and the forming mechanism for compound structure of its special cases. Especially, with the help of the Project Method, its Hopf bifurcation of codimension one is in detailed formulated. Numerical simulation results not only examine the corresponding theoretical analytical results, but also show that this system possesses abundant and complex dynamical properties not solved theoretically, which need further attention.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.3
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• pp.466-471
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• 2012

In this paper, we consider the problem of a robust passive filtering with low-order for discrete-time singular systems with polytopic uncertainties. A BRL(bounded real lemma) for robust passivity with a dissipativity of discrete-time uncertain singular systems is derived. A low-order robust passive filter design method is proposed by new reduced-order method and LMI(linear matrix inequality) technique on the basis of the obtained BRL. Finally, illustrative examples are presented to show the applicability of the proposed method.