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11
On averaging for switched linear differential algebraic equations
"... Averaging is an effective technique which allows the analysis and control design of nonsmooth switched systems through the use of corresponding simpler smooth averaged systems. Approximation results and stability analysis have been presented in the literature for dynamic systems described by switch ..."
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Cited by 7 (5 self)
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Averaging is an effective technique which allows the analysis and control design of nonsmooth switched systems through the use of corresponding simpler smooth averaged systems. Approximation results and stability analysis have been presented in the literature for dynamic systems described by switched ordinary differential equations. In this paper the averaging technique is shown to be useful also for the analysis of switched systems whose modes are represented by means of differential algebraic equations (DAEs). An approximation result is derived for a simple but representative homogenous switched DAE with periodic switching signals and two modes. Simulations based on a simple electrical circuit model illustrate the theoretical result.
Averaging of nonsmooth systems using dither
, 2006
"... It was shown by Zames and Shneydor and later by Mossaheb that a highfrequency dither signal of a quite arbitrary shape can be used to narrow the effective nonlinear sector of Lipschitz continuous feedback systems. In this paper, it is shown that also discontinuous nonlinearities of feedback systems ..."
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Cited by 6 (2 self)
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It was shown by Zames and Shneydor and later by Mossaheb that a highfrequency dither signal of a quite arbitrary shape can be used to narrow the effective nonlinear sector of Lipschitz continuous feedback systems. In this paper, it is shown that also discontinuous nonlinearities of feedback systems can be narrowed using dither, as long as the amplitude distribution function of the dither is absolutely continuous and has bounded derivative. The averaged system is proven to approximate the dithered system with an error of the order of dither period.
An Overview on Averaging for Pulsemodulated Switched Systems
, 2011
"... Averaging of fast switching systems is an effective technique used in many engineering applications. Practical stability and control design for a nonsmooth switched system can be inferred by analyzing the smooth averaged system. In this paper we overview the few formal approaches proposed in the li ..."
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Cited by 6 (4 self)
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Averaging of fast switching systems is an effective technique used in many engineering applications. Practical stability and control design for a nonsmooth switched system can be inferred by analyzing the smooth averaged system. In this paper we overview the few formal approaches proposed in the literature to deal with the averaging of nonsmooth systems. The dithering, the phasor dynamics and the hybrid framework techniques are recast and compared by considering pulsemodulated switched linear systems as the common modeling platform.
Iss properties of nonholonomic vehicles
 Systems & Control Letters
"... The paper presents the first result on nonholonomic systems enjoying Input to State Stability (ISS) properties. Although it is known that smooth stabilizability implies ISS, the converse is not generally true. This leaves the possibility of non smoothly stabilizable systems being ISS with respect to ..."
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Cited by 5 (0 self)
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The paper presents the first result on nonholonomic systems enjoying Input to State Stability (ISS) properties. Although it is known that smooth stabilizability implies ISS, the converse is not generally true. This leaves the possibility of non smoothly stabilizable systems being ISS with respect to a particular input, after an appropriate feedback transformation. This is shown to be true for the case of the unicycle with a dynamic extension, in a particular topology induced by a metric appropriate for this type of systems. A feedback control law renders the closed loop system locally ISS in the particular topology. Potential applications include stability and robustness analysis of formations of mobile robots. 1
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.
An averaging result for switched DAEs with multiple modes
"... The major motivation of the averaging technique for switched systems is the construction of a smooth average system whose state trajectory approximates in some sense the state trajectory of the switched system. Averaging of dynamic systems represented by switched ordinary differential equations (OD ..."
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Cited by 3 (3 self)
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The major motivation of the averaging technique for switched systems is the construction of a smooth average system whose state trajectory approximates in some sense the state trajectory of the switched system. Averaging of dynamic systems represented by switched ordinary differential equations (ODEs) has been widely analyzed in the literature. The averaging approach can be useful also for the analysis of switched differential algebraic equations (DAEs). Indeed by analyzing the evolution of the switched DAEs state it is possible to conjecture the existence of an average model. However a trivial generalization of the ODE case is not possible due to the presence of state jumps. In this paper we discuss the averaging approach for switched DAEs and an approximation result is derived for homogenous switched linear DAE with periodic switching signals commuting among several modes. This approximation result extends a recent averaging result for switched DAEs with only two modes. Numerical simulations confirm the validity of the averaging approach for switched DAEs.
Averaging for Switched DAEs: Convergence, Partial Averaging and Stability
, 2015
"... Averaging is a useful technique to simplify the analysis of switched systems. In this paper we present averaging results for the class of systems described by switched differential algebraic equations (DAEs). Conditions on the consistency projectors are given which guarantee convergence towards a no ..."
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Cited by 1 (1 self)
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Averaging is a useful technique to simplify the analysis of switched systems. In this paper we present averaging results for the class of systems described by switched differential algebraic equations (DAEs). Conditions on the consistency projectors are given which guarantee convergence towards a nonswitched averaged system. A consequence of this result is the possibility to stabilize switched DAEs via fast switching. We also study partial averaging in case the consistency projectors do not satisfy the conditions for convergence; the averaged system is then still a switched system, but is simpler than the original. The practical interest of the theoretical averaging results is demonstrated through the analysis of the dynamics of a switched electrical circuit.
Conditions on the dither shape in the averaging of switched systems
, 2003
"... It was shown by Zames and Shneydor that a highfrequency dither of a quite arbitrary shape can be used to smooth the effective nonlinear sector of Lipschitz continuous feedback systems. Here it is shown that also systems with discontinuous nonlinearities can be smoothed using dither signals, as lon ..."
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It was shown by Zames and Shneydor that a highfrequency dither of a quite arbitrary shape can be used to smooth the effective nonlinear sector of Lipschitz continuous feedback systems. Here it is shown that also systems with discontinuous nonlinearities can be smoothed using dither signals, as long as the amplitude distribution function of the dither is Lipschitz continuous.
SUBTLETIES IN THE AVERAGING OF HYBRID SYSTEMS WITH APPLICATIONS TO POWER ELECTRONICS
"... Abstract: Dither signals are commonly used in electronics for implementing different type of modulations in power converters, which represent a very interesting class of hybrid systems. It was recently shown that a nonsmooth dithered system can be approximated by an averaged system provided that the ..."
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Abstract: Dither signals are commonly used in electronics for implementing different type of modulations in power converters, which represent a very interesting class of hybrid systems. It was recently shown that a nonsmooth dithered system can be approximated by an averaged system provided that the dither frequency is sufficiently high and that the amplitude distribution function of the dither is absolutely continuous and has bounded derivative. This result is exploited in this paper for power converters. Averaged models corresponding to various shapes of dither signal are analyzed, showing that dither with Lipschitz continuous amplitude distribution function can be used to adapt the equivalent gain of the power converter. 1.