Erfurt, Germany
Erfurt, Germany

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Dashkovskiy S.,FH Erfurt | Kosmykov M.,University of Bremen
Automatica | Year: 2013

We consider the interconnections of arbitrary topology of a finite number of ISS hybrid systems and study whether the ISS property is maintained for the overall system. We show that if the small gain condition is satisfied, then the whole network is ISS and show how a non-smooth ISS-Lyapunov function can be explicitly constructed in this case. © 2013 Elsevier Ltd. All rights reserved.

Dashkovskiy S.,FH Erfurt | Mironchenko A.,University of Bremen
Mathematics of Control, Signals, and Systems | Year: 2013

We develop tools for investigation of input-to-state stability (ISS) of infinite-dimensional control systems. We show that for certain classes of admissible inputs, the existence of an ISS-Lyapunov function implies the ISS of a system. Then for the case of systems described by abstract equations in Banach spaces, we develop two methods of construction of local and global ISS-Lyapunov functions. We prove a linearization principle that allows a construction of a local ISS-Lyapunov function for a system, the linear approximation of which is ISS. In order to study the interconnections of nonlinear infinite-dimensional systems, we generalize the small-gain theorem to the case of infinite-dimensional systems and provide a way to construct an ISS-Lyapunov function for an entire interconnection, if ISS-Lyapunov functions for subsystems are known and the small-gain condition is satisfied. We illustrate the theory on examples of linear and semilinear reaction-diffusion equations. © 2012 Springer-Verlag London Limited.

Dashkovskiy S.,FH Erfurt | Kosmykov M.,University of Bremen | Mironchenko A.,University of Bremen | Naujok L.,University of Bremen
Nonlinear Analysis: Hybrid Systems | Year: 2012

In this paper, we consider the input-to-state stability (ISS) of impulsive control systems with and without time delays. We prove that, if the time-delay system possesses an exponential Lyapunov-Razumikhin function or an exponential Lyapunov-Krasovskii functional, then the system is uniformly ISS provided that the average dwell-time condition is satisfied. Then, we consider large-scale networks of impulsive systems with and without time delays and prove that the whole network is uniformly ISS under the small-gain and the average dwell-time condition. Moreover, these theorems provide us with tools to construct a Lyapunov function (for time-delay systems, a Lyapunov-Krasovskii functional or a Lyapunov-Razumikhin function) and the corresponding gains of the whole system, using the Lyapunov functions of the subsystems and the internal gains, which are linear and satisfy the small-gain condition. We illustrate the application of the main results on examples. © 2012 Elsevier Ltd.

Ito H.,Kyushu Institute of Technology | Dashkovskiy S.,FH Erfurt | Wirth F.,University of Wrzburg
Automatica | Year: 2012

This paper addresses the problem of verifying stability of networks whose subsystems admit dissipation inequalities of integral input-to-state stability (iISS). We focus on two ways of constructing a Lyapunov function satisfying a dissipation inequality of a given network. Their difference from one another is elucidated from the viewpoint of formulation, relation, fundamental limitation and capability. One is referred to as the max-type construction resulting in a Lipschitz continuous Lyapunov function. The other is the sum-type construction resulting in a continuously differentiable Lyapunov function. This paper presents geometrical conditions under which the Lyapunov construction is possible for a network comprising n<2 subsystems. Although the sum-type construction for general n>2 has not yet been reduced to a readily computable condition, we obtain a simple condition of iISS small gain in the case of n=2. It is demonstrated that the max-type construction fails to offer a Lyapunov function if the network contains subsystems which are not input-to-state stable (ISS). © 2012 Elsevier Ltd. All rights reserved.

Dashkovskiy S.,FH Erfurt | Ito H.,Kyushu Institute of Technology | Wirth F.,University of Würzburg
European Journal of Control | Year: 2011

In this paper we consider the stability of networks consisting of nonlinear ISS systems supplied with ISS Lyapunov functions defined in dissipative form. The problem of constructing an ISS Lyapunov function for the network is addressed. Our aim is to provide a geometrical condition of a small gain type under which this construction is possible and to describe a method of an explicit construction of such an ISS Lyapunov function. In the dissipative form, the geometrical approach allows us to discuss both Lipschitz continuous construction and continuously differentiable construction of ISS Lyapunov functions. © 2011 EUCA.

Ito H.,Kyushu Institute of Technology | Jiang Z.-P.,New York University | Dashkovskiy S.N.,FH Erfurt | Ruffer B.S.,University of Paderborn
IEEE Transactions on Automatic Control | Year: 2013

This paper gives a solution to the problem of verifying stability of networks consisting of integral input-to-state stable (iISS) subsystems. The iISS small-gain theorem developed recently has been restricted to interconnections of two subsystems. For large-scale systems, stability criteria relying only on gain-type information that were previously developed address only input-to-state stable (ISS) subsystems. To address the stability problem involving iISS subsystems interconnected in general structure, this paper shows how to construct Lyapunov functions of the network by means of a sum of nonlinearly rescaled individual Lyapunov functions of subsystems under an appropriate small-gain condition. © 2012 IEEE.

Polushin I.G.,University of Western Ontario | Dashkovskiy S.N.,FH Erfurt | Takhmar A.,University of Western Ontario | Patel R.V.,University of Western Ontario
Automatica | Year: 2013

For cooperative force-reflecting teleoperation over networks, conventional passivity-based approaches have limited applicability due to nonpassive slave-slave interactions and irregular communication delays imposed by networks. In this paper, a small gain framework for stability analysis design of cooperative network-based force reflecting teleoperator systems is developed. The framework is based on a version of weak input-to-output practical stability (WIOPS) nonlinear small gain theorem that is applicable to stability analysis of large-scale network-based interconnections. Based on this result, we design a cooperative force-reflecting teleoperator system which is guaranteed to be stable in the presence of multiple network-induced communication constraints by appropriate adjustment of local control gains and/or force-reflection gains. Experimental results are presented that confirm the validity of the proposed approach. © 2012 Elsevier Ltd. All rights reserved.

Agency: European Commission | Branch: FP7 | Program: CP-FP | Phase: TPT.2011.1-2. | Award Amount: 828.21K | Year: 2011

Addressing the needs of older people in the development of future transportation concepts in Europe is an important issue. However, there are no systematic studies available, which provide a complete picture of what has already been done to adress the mobility-related needs of the elderly. Such a systematic study could be used to create an Action Plan for future steps in addressing the needs of an ageing society in mobility and transportation. With TRACY, we seek to provide a systematic and comprehensive study of current activity, and use the results of this study to analyse the present situation, identify research gaps and contribute towards a strategy to tackle the challenge of transport in an ageing society. Indeed, in the context of the need to contribute to a better understanding of the requirements to properly address elderly mobility (work programme 2011 cooperation theme 7 transport (including aeronautics) p. 101), our overarching aim is to develop an Action Plan outlining means of proceeding to achieve excellence in transport for an ageing society, on the basis of a detailed analysis of a comprehensive dataset. This Action Plan will include guidelines, requirements and specifications to promote safe and adequate usage of all passenger land transport modes for older people. Recommendations will be made in the form of specific research topics for European and national RTD programmes. In our concept we pay special attention to the gendered nature of the issue at hand, as well as to human factors such as geographical and cultural or welfare differences, and possible conflicts between social and other aspects of sustainability (e.g. environmental). This objectives will be achieved by document review and synthesis completed by Interviews with European national transport authorities, followed by an critical analysis of the mobility needs and practices of elderly people and the assessment of the effectiveness of current policies. One significant output is the bigger picture of transport in an ageing society.

Urban parks can be invasion sources through planting of introduced taxa. On the other hand, parks may act as hot spots of biodiversity in urban areas and can support the preservation of endangered and rare taxa. Even if historic urban parks are evaluated first of all as heritage sites, they are also credited for their ecosystem services and positive aesthetical and social values.Although there are numerous studies in Europe on the design, philosophies and historical background of parks as well as their biological diversity, little research has posed the question of how landscape design principles have influenced the biological conservation value of parks. Because the landscape park style was one of the most influential historical landscape design fashions in Europe we focused our study on the 'Park an der Ilm' in Weimar, Germany which was created in the late 18th century and is since 1998 part of the UNESCO World heritage.Our research questions were: 1.Which design principles, plant material and technical implementation were used during the creation and management of the park?2.What is the current value of the park for biological conservation especially for the conservation of endangered plant species and habitats?3.What is the relationship between design principles and the present-day value of the park?We compared our results with similar landscape parks and made suggestions for future sustainable park design, restoration and management. © 2012 Elsevier B.V.

Dashkovskiy S.,FH Erfurt | Pavlichkov S.,FH Erfurt
Mathematics of Control, Signals, and Systems | Year: 2012

We solve the problem of global uniform input-to-state stabilization with respect to external disturbance signals for a class of large-scale interconnected nonlinear switched systems. The overall system is composed of switched subsystems each of which has the nonlinear MIMO generalized triangular form, which (in contrast to strict-feedback form) has non-invertible input-output maps. The switching signal is an arbitrary unknown piecewise constant function and the feedback constructed does not depend on the switching signal. © 2012 Springer-Verlag London Limited.

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