Results 1  10
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22
Fast switches in relay feedback systems
 AUTOMATICA 35 (1999) 539—552
, 1999
"... Relays are common in automatic control systems. Even linear systems with relay feedback are, however, far from fully understood. New results are given about the behavior of these systems via a statespace approach. It is proved that there exist multiple fast switches if and only if the sign of the ..."
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Cited by 29 (6 self)
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Relays are common in automatic control systems. Even linear systems with relay feedback are, however, far from fully understood. New results are given about the behavior of these systems via a statespace approach. It is proved that there exist multiple fast switches if and only if the sign of the first nonvanishing Markov parameter of the linear system is positive. Fast switches are shown to occur as part of stable limit cycles. An analysis is developed for these limit cycles that illustrates how they can be predicted.
Selfoscillations and sliding in relay feedback systems: Symmetry and bifurcations
 INT. J. BIFURCATION & CHAOS
, 2001
"... This paper is concerned with the bifurcation analysis of linear dynamical systems with relay feedback. The emphasis is on the bifurcations of the system periodic solutions and their symmetry. It is shown that, despite what has been conjectured in the literature, a symmetric and unforced relay feedba ..."
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Cited by 25 (9 self)
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This paper is concerned with the bifurcation analysis of linear dynamical systems with relay feedback. The emphasis is on the bifurcations of the system periodic solutions and their symmetry. It is shown that, despite what has been conjectured in the literature, a symmetric and unforced relay feedback system can exhibit asymmetric periodic solutions. Moreover, the occurrence of periodic solutions characterized by one or more sections lying within the system discontinuity set is outlined. The mechanisms underlying their formation are carefully studied and shown to be due to an interesting, novel class of local bifurcations.
SLIDING MOTION IN FILIPPOV DIFFERENTIAL SYSTEMS: THEORETICAL RESULTS AND A COMPUTATIONAL APPROACH
"... Abstract. In this work, we discuss some theoretical and numerical aspects of solving differential equations with discontinuous righthand sides of Filippov type. In particular: (i) we propose second order corrections to the theory of Filippov, (ii) we provide a systematic and nonambiguous way to de ..."
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Cited by 12 (1 self)
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Abstract. In this work, we discuss some theoretical and numerical aspects of solving differential equations with discontinuous righthand sides of Filippov type. In particular: (i) we propose second order corrections to the theory of Filippov, (ii) we provide a systematic and nonambiguous way to define the vector field on the intersection of several surfaces of discontinuity, and (iii) we propose, and implement, a numerical method to approximate a trajectory of systems with discontinuous righthand sides, and illustrate its performance on a few examples. 1.
Dither for smoothing relay feedback systems
 IEEE Trans. on Circuits and SystemsI: Fundamental Theory and Applications
, 2003
"... Dither signals are commonly used for compensating nonlinearities in feedback systems in electronics and mechanics. The seminal works by Zames and Shneydor and more recently by Mossaheb present rigorous tools for systematic design of dithered systems. Their results rely however on a Lipschitz assumpt ..."
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Cited by 7 (5 self)
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Dither signals are commonly used for compensating nonlinearities in feedback systems in electronics and mechanics. The seminal works by Zames and Shneydor and more recently by Mossaheb present rigorous tools for systematic design of dithered systems. Their results rely however on a Lipschitz assumption on the nonlinearity and thus do not cover important applications with discontinuities. The aim of this thesis is to provide some ideas and tools on how to analyse and design dither in nonsmooth systems. In particular, it is shown that a dithered relay feedback system can be approximated by a smoothed system. Guidelines are given for tuning the amplitude and the period time of the dither signal, in order to stabilize the nonsmooth system. Stability results based on Popovlike and ZamesFalb criteria jointly with some Linear Matrix Inequalities are proposed. Moreover it is argued that in dithered relay feedback systems the shape of dither signals is relevant for stabilization. Some peculiar behaviours of relay feedback systems dithered with a particular class of dither signals are presented. When the dither signal is a square wave, the dithered system can exhibit an asymmetric periodic orbit, though the smoothed system is asymptotically stable. We even show an example in which, by using a trapezoidal dither signal, both systems have a stable oscillation, but the period time for the oscillation of the smoothed system is different from the one of the dithered system. Finally some engineering applications are presented in order to show the usefulness of techniques and results discussed in the thesis. Thesis Supervisor: Franco Garofalo, Professor of Automatic Control Thesis Supervisor: Francesco Vasca, Associate Professor of Automatic Control Acknowledgements Yes, ...it's fina...
ON THE ROBUSTNESS OF PERIODIC SOLUTIONS IN RELAY FEEDBACK SYSTEMS
 15TH TRIENNIAL WORLD CONGRESS, BARCELONA, SPAIN
"... Structural robustness of limit cycles in relay feedback systems is studied. Motivated by a recent discovery of a novel class of bifurcations in these systems, it is illustrated through numerical simulation that small relay perturbations may change the appearance of closed orbits dramatically. It i ..."
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Cited by 5 (1 self)
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Structural robustness of limit cycles in relay feedback systems is studied. Motivated by a recent discovery of a novel class of bifurcations in these systems, it is illustrated through numerical simulation that small relay perturbations may change the appearance of closed orbits dramatically. It is shown analytically that certain stable periodic solutions in relay feedback systems are robust to relay perturbations.
HYBRID LIMIT CYCLES AND HYBRID POINCARÉBENDIXSON
, 2002
"... We present two results about regular hybrid systems with no branching (Simić et al., 2000a). The first one provides a condition for asymptotic stability of hybrid closed orbits in terms of contractionexpansion rates of resets and flows in a hybrid system. The second one is a generalization of the ..."
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Cited by 4 (2 self)
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We present two results about regular hybrid systems with no branching (Simić et al., 2000a). The first one provides a condition for asymptotic stability of hybrid closed orbits in terms of contractionexpansion rates of resets and flows in a hybrid system. The second one is a generalization of the PoincaréBendixson theorem to planar hybrid systems.
On the Averaging of a Class of Hybrid Systems
, 2004
"... Modeling abstraction and timescale separation in the design of complex systems often leads to hybrid dynamics. Discontinuities in the continuous evolution of a hybrid system may however create difficulties in the formal analysis, as well as in numerical simulation and verification. Here we study a ..."
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Cited by 3 (2 self)
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Modeling abstraction and timescale separation in the design of complex systems often leads to hybrid dynamics. Discontinuities in the continuous evolution of a hybrid system may however create difficulties in the formal analysis, as well as in numerical simulation and verification. Here we study a class of hybrid systems that are excited by highfrequency external signals. These systems arise in the modeling of switched power converters, mechanical systems with friction and quantized systems. For a quite general class of excitation signals, an averaging result is shown stating that the hybrid system can be approximated by a Lipschitzcontinuous system. The approximation is in the order of the maximal repetition interval of the excitation signal.
FUNDAMENTAL MATRIX SOLUTIONS OF PIECEWISE SMOOTH DIFFERENTIAL SYSTEMS
, 2009
"... We consider the fundamental matrix solution associated to piecewise smooth differential systems of Filippov type, in which the vector field varies discontinuously as solution trajectories reach one or more surfaces. We review the cases of transversal intersection and of sliding motion on one surfa ..."
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Cited by 1 (0 self)
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We consider the fundamental matrix solution associated to piecewise smooth differential systems of Filippov type, in which the vector field varies discontinuously as solution trajectories reach one or more surfaces. We review the cases of transversal intersection and of sliding motion on one surface. We also consider the case when sliding motion takes place on the intersection of two or more surfaces. Numerical results are also given.