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See detailGlobal analysis of piecewise linear systems using impact maps and quadratic surface Lyapunov functions
Goncalves, Jorge UL; Megretski, A.; Dahleh, M.

in IEEE Transactions on Automatic Control (2003), 48(12), 2089-2106

This paper presents an entirely new constructive global analysis methodology for a class of hybrid systems known as piecewise linear systems (PLS). This methodology infers global properties of PLS solely ... [more ▼]

This paper presents an entirely new constructive global analysis methodology for a class of hybrid systems known as piecewise linear systems (PLS). This methodology infers global properties of PLS solely by studying the behavior at switching surfaces associated with PLS. The main idea is to analyze impact maps, i.e., maps from one switching surface to the next switching surface. Such maps are known to be “unfriendly” maps in the sense that they are highly nonlinear, multivalued, and not continuous. We found, however, that an impact map induced by an linear time-invariant flow between two switching surfaces can be represented as a linear transformation analytically parametrized by a scalar function of the state. This representation of impact maps allows the search for surface Lyapunov functions (SuLF) to be done by simply solving a semidefinite program, allowing global asymptotic stability, robustness, and performance of limit cycles and equilibrium points of PLS to be efficiently checked. This new analysis methodology has been applied to relay feedback, on/off and saturation systems, where it has shown to be very successful in globally analyzing a large number of examples. In fact, it is still an open problem whether there exists an example with a globally stable limit cycle or equilibrium point that cannot be successfully analyzed with this new methodology. Examples analyzed include systems of relative degree larger than one and of high dimension, for which no other analysis methodology could be applied. This success in globally analyzing certain classes of PLS has shown the power of this new methodology, and suggests its potential toward the analysis of larger and more complex PLS. [less ▲]

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See detailUnderstanding the differences between how novice and experienced designers approach design tasks
Ahmed, S.; Wallace, K. M.; Blessing, Lucienne UL

in Research in Engineering Design (2003), 14(1), 1-11

Research was undertaken to understand how to provide the most appropriate support for novice designers in engineering design. However, how designers apply their experience and knowledge is not understood ... [more ▼]

Research was undertaken to understand how to provide the most appropriate support for novice designers in engineering design. However, how designers apply their experience and knowledge is not understood and further research in this area is required. This paper describes an observational study to understand how novice and experienced designers approach design tasks. [less ▲]

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See detailFuture Issues in Design Research
Blessing, Lucienne UL

in Lindemann, Udo (Ed.) Human Behaviour in Design. Individuals, Teams, Tools (2003)

This chapter contains in its first part the core future issues I derived from the presentations and discussion sessions at the conference on "Human Behvaiour and Design : Individuals, Teams, Tools" as ... [more ▼]

This chapter contains in its first part the core future issues I derived from the presentations and discussion sessions at the conference on "Human Behvaiour and Design : Individuals, Teams, Tools" as well as personal reflections. The second part presents my personal views on the most urgent issues in the area of human behaviour in design, and ways to proceed. [less ▲]

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See detailLes modes opéatoires de la cryptographie symétrique
Schiltz, Jang UL

Report (2003)

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See detailRegions of Stability for Limit Cycles of Piecewise Linear Systems
Goncalves, Jorge UL

in Proceedings of the 42th IEEE Conference on Decision and Control (2003)

This paper starts by presenting local stability conditions for limit cycles of piecewise linear systems (PLS), based on analyzing the linear part of Poincare maps. Local stability guarantees the existence ... [more ▼]

This paper starts by presenting local stability conditions for limit cycles of piecewise linear systems (PLS), based on analyzing the linear part of Poincare maps. Local stability guarantees the existence of an asymptotically stable neighborhood around the limit cycle. However, tools to characterize such neighborhood do not exist. This work gives conditions in the form of LMIs that guarantee asymptotic stability of PLS in a reasonably large region around a limit cycle, based on recent results on impact maps and surface Lyapunov functions (SuLF). These are exemplified with a biological application: a 4th-order neural oscillator, also used in many robotics applications like, for example, juggling and locomotion. [less ▲]

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See detailGlobal Asymptotic Stability of Oscillations with Sliding Modes
Goncalves, Jorge UL

in Proceedings of the 15th IFAC World Congress (2003)

This paper explores a new methodology based on quadratic surface Lyapunov functions to globally analyze oscillations with sliding modes in relay feedback systems (RFS). The method consists in efficiently ... [more ▼]

This paper explores a new methodology based on quadratic surface Lyapunov functions to globally analyze oscillations with sliding modes in relay feedback systems (RFS). The method consists in efficiently construct quadratic Lyapunov functions on switching surfaces that can be used to show that impact maps, i.e., maps from one switch to the next, are contracting. This, in turn, shows that the system is globally stable. Several classes of piecewise linear systems (PLS) were previously successfully analyzed with this methodology. In this paper, we consider PLS whose trajectories switch between subsystems of different dimensions. We present and discuss distinct relaxations leading to sufficient conditions of different conservatism and computationally complexity. The results in this paper open the door to the analysis of other, more complex classes of PLS. [less ▲]

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See detailRe-Interpretation of Conceptualisation - A Contribution to the Advance of Design Theory
Bender, Bernd; Blessing, Lucienne UL

in Lindemann, Udo (Ed.) Human Behaviour in Design. Individuals, Teams, Tools (2003)

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