By Laurent Fribourg, Romain Soulat

This ebook offers correct-by-design regulate recommendations for switching platforms, utilizing various equipment of balance research. Switching structures are more and more utilized in the electronics and mechanical industries; in strength electronics and the car undefined, for instance. this is often because of their flexibility and ease in competently controlling commercial mechanisms. by means of adopting applicable regulate ideas, we will be able to steer a switching procedure to a sector based at a wanted equilibrium element, whereas heading off “unsafe” areas of parameter saturation.
The authors clarify a number of correct-by-design equipment for keep watch over synthesis, utilizing various tools of balance and invariance research. additionally they offer numerous purposes of those how you can commercial examples of energy electronics.


1. keep watch over concept: uncomplicated Concepts.
2. Sampled Switched Systems.
3. defense Controllers.
4. balance Controllers.
5. program to Multilevel Converters.
6. different concerns: Reachability, Sensitivity, Robustness and Nonlinearity.

About the Authors

Laurent Fribourg is head of the LSV (Laboratoire Spécification et Vérification) and clinical Coordinator of the Institut Farman, Institut Fédératif de Recherche CNRS, which brings jointly the services of 5 laboratories from ENS Cachan, in France, within the fields of modeling, simulation and validation of advanced platforms. He has released over 70 articles in foreign journals and reviewed lawsuits of overseas meetings, within the area of the speculation of formal tools and their commercial applications.
Romain Soulat is within the 3rd yr of his doctorate on the LSV at ENS Cachan in France, less than the supervision of Laurent Fribourg. he's engaged on the modeling and verification of hybrid platforms. specifically, his pursuits obstacle robustness in scheduling difficulties – specially as a part of a collaborative venture with EADS Astrium at the verification of an element within the launcher for the longer term Ariane 6 rocket. He has released five articles in reviewed court cases of foreign conferences.

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Additional info for Control of Switching Systems by Invariance Analysis: Applcation to Power Electronics

Sample text

The problem is closely related to the problem of finding a controlled invariant subset of R that is as small as possible, ideally minimal. We present a direct forward-oriented method that decomposes a given state region R, and induces a state-dependent control that makes the trajectories of the system converge to finite sets of points that, under certain conditions, correspond to limit cycles. The method can also be used for synthesizing safety controllers in order to prove safety properties. 2).

Zonotopes allow us to compute easily over-approximations of the successor sets in order to take into account small perturbations (or uncertainties) of the system dynamics. All the dynamics of the system are now of the form x(t) ˙ = Au x(t) + bu + ε(t), where ε(t) represents disturbance under the form of a vector belonging to a given box Sampled Switched Systems 23 Λ = [−ε1 , +ε1 ] × · · · × [−εn , +εn ] of Rn , with εi ≥ 0 for i = 1, . . , n. We will use x(t, x, u,ε ) to denote the point reached by the system at time t under mode u with disturbance ε, from the initial condition x.

Consider a switched system Σ = (τ, U, F ), a desired precision ε and a time sampling value τ . Under certain Lyapunov-based stabilization conditions, it is shown in [GIR 10b] that there exists a space sampling 32 Control of Switching Systems by Invariance Analysis value η such that the transition systems of Σ and Ση are approximately bisimilar with precision ε. In the context of S 2 -systems, the conditions of Lyapunov-based stabilization can be simplified as follows. – Consider a switched system Σ = (τ, U, F ), a desired precision ε and a time sampling value τ .

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