Abstract
Affine hybrid systems are hybrid systems in which the discrete domains are affine sets and the transition maps between discrete domains are affine transformations. The simple structure of these systems results in interesting geometric properties; one of these is the notion of spatial equivalence. In this paper, a formal framework for describing affine hybrid systems is introduced. As an application, it is proven that every compact hybrid system H is spatially equivalent to a hybrid system H id in which all the transition maps are the identity. An explicit and computable construction for H id is given.
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Ames, A.D., Sastry, S.: Affine hybrid systems: part 1. UC Berkeley ERL Technical Memorandum, available at http://www.eecs.berkeley.edu/~adames/AffineHybridSystemsPart1.pdf
Ames, A.D., Sastry, S.: Affine hybrid systems: part 2. UC Berkeley ERL Technical Memorandum, available at http://www.eecs.berkeley.edu/~adames/AffineHybridSystemsPart2.pdf
Ames, A.D., Sastry, S.: Givens Rotations and SO(n). Submitted to ACM Symposium on Computational Geometry (2004)
Bemporad, A., Ferrari-Trecate, G., Morari, M.: Observability and controllability of piecewise affine and hybrid systems. IEEE Transactions on Automatic Control 45(10), 1864–1876 (2000)
Golub, G., Loan, C.V.: Matrix Computation. Johns Hopkins University Press, Baltimore (1996)
Jirstrand, M.: Invariant sets for a class of hybrid systems. In: Proceedings of the 37th IEEE Conference on Decision and Control. Tampa, FL (December 1998)
Johansson, M., Rantzer, A.: On the computation of piecewise quadratic Lyapunov functions. In: Proceedings of the 36th IEEE Conference on Decision and Control. San Diego, CA (December 1997)
Meyer, C.: Matrix analysis and applied linear algebra. SIAM, Philadelphia (2000)
Simic, S.N., Johansson, K.H., Lygeros, J., Sastry, S.: Towards a Geometric Theory of Hybrid Systems. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 421–436. Springer, Heidelberg (2000)
Sun, Z., Zheng, D.: On reachability and stabilization of switched linear systems. IEEE Transactions on Automatic Control 46(2), 291–295 (2001)
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Ames, A.D., Sastry, S. (2004). Affine Hybrid Systems. In: Alur, R., Pappas, G.J. (eds) Hybrid Systems: Computation and Control. HSCC 2004. Lecture Notes in Computer Science, vol 2993. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24743-2_2
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DOI: https://doi.org/10.1007/978-3-540-24743-2_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21259-1
Online ISBN: 978-3-540-24743-2
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