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A Generalized Approach for Analysis and Control of Discrete-Time Piecewise Affine and Hybrid Systems

  • Francesco Alessandro Cuzzola
  • Manfred Morari
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2034)

Abstract

In this paper we investigate some analysis and control problems for discrete-time hybrid systems in the piece-wise affine form. By using arguments from the dissipativity theory for nonlinear systems, we show that H analysis and synthesis problems can be formulated and solved via Linear Matrix Inequalities by taking into account the switching structure of the considered system. In this paper we address the generalized problem of controlling hybrid systems whose switching structure does not depend only on the state but also on the control input.

Keywords

Hybrid System Lyapunov Function Linear Matrix Inequality Model Predictive Control Synthesis Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Bemporad, A., Morari, M.: Control of Systems Integrating Logic, Dynamics, and Constraints. Automatica, 35(3), (1999), 407–427.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bemporad, A., Morari, M., Dua, V., Pistikopoulos, E. N.: The Explicit Linear Quadratic Regulator for Constrained Systems. American Control Conference, Chicago, IL, (2000).Google Scholar
  3. 3.
    Bemporad, A., Ferrari-Trecate, G., Morari, M.: Observability and Controllability of Piecewise Affine and Hybrid Systems. IEEE Transactions on Automatic Control, 45(10), (2000), 1864–1876.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Bemporad, A., Torrisi, F.D., Morari, M.: Optimization-Based Verification and Stability Characterization of Piecewise Affine and Hybrid Systems. Proceedings 3rd International Workshop on Hybrid Systems, Lecture Notes in Computer Science, Springer-Verlag, Pittsburgh, USA (2000).Google Scholar
  5. 5.
    Byrnes, C. I., Lin, W.: Passivity and absolute stabilization of a class of discretetime nonlinear systems. Automatica, 31(2), (1995), 263–268.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    de Oliveira, M. C., Bernussou, J., Geromel, J. C.: A new discrete-time robust stability condition. System & Control Letters, 37, (1999), 261–265.zbMATHCrossRefGoogle Scholar
  7. 7.
    Ferrari-Trecate, G., Cuzzola, F. A., Mignone, D., Morari, M.: Analysis of Discrete-Time Piecewise Affine and Hybrid Systems. Submitted for publication.Google Scholar
  8. 8.
    Gahinet, P., Nemirowski, A., Laub, A. J., Chilali, M.: LMI Control Toolbox, The MathWorks Inc., (1994).Google Scholar
  9. 9.
    Heemels, W.P.M.H., De Schutter, B.: On the Equivalence of Classes of Hybrid Systems: Mixed Logical Dynamical and Complementarity Systems. T.R. 00 I/04, Technische Universiteit Eindhoven, (2000).Google Scholar
  10. 10.
    Heiming, B., Lunze, J.: Definition of the Three-Tank Benchmark Problem for Controller Reconfiguration, European Control Conference, Karlshrue, Germany, (1999).Google Scholar
  11. 11.
    Johansen, T. A.: Computation of Lyapunov functions for smooth nonlinear systems using convex optimisation. Automatica, 36, (2000), 1617–1626.zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Johansson, M., Rantzer, A.: Computation of Piecewise Quadratic Lyapunov Functions for Hybrid Systems. IEEE Transactions on Automatic Control, 43(4), (2000), 555–559.CrossRefMathSciNetGoogle Scholar
  13. 13.
    Johansson, M., Rantzer, A.: Piecewise Linear Quadratic Optimal Control. IEEE Transactions on Automatic Control, 43(4), (2000), 629–637.MathSciNetGoogle Scholar
  14. 14.
    Lin, W., Byrnes, C. I.: H1 Control of Discrete-Time Nonlinear Systems. IEEE Transactions on Automatic Control, 41(4), (1996), 494–510.zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Mignone, D., Ferrari-Trecate, G., Morari, M.: Stability and Stabilization of Piecewise Affine and Hybrid Systems: An LMI Approach, IEEE Conference on Decision and Control, Sydney, Australia, (2000).Google Scholar
  16. 16.
    Scherer, C. W., Gahinet, P., Chilali, M.: Multi-Objective Output-Feedback Control via LMI Optimization. IEEE Transactions on Automatic Control, 42(7), (1997), 896–911.zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Sontag, E.D.: Interconnected automata and linear systems: A theoretical framework in discrete-time. Hybrid Systems III-Verification and Control, R. Alur, T.A. Henzinger and E.D. Sontag eds., 1066, Lecture Notes in Computer Science. Springer-Verlag, Pittsburgh, USA, (1996), 436–448.Google Scholar
  18. 18.
    Van der Schaft, A. J.: L 2-gain analysis of nonlinear systems and nonlinear H∓ control, IEEE Transactions on Automatic Control, 37, (1992), 770–784.zbMATHCrossRefGoogle Scholar
  19. 19.
    Willems, J. C.: Dissipative dynamic systems, Arch. Rational Mechanics Analysis, 45, (1972), 321–393.zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Yakubovich, V. A.: S-Procedure in nonlinear control theory. Vestnik Leninggradskogo Universiteta, Ser. Matematika, (1971), 62–77.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Francesco Alessandro Cuzzola
    • 1
  • Manfred Morari
    • 1
  1. 1.Institut für Automatik, ETH - Swiss Federal Institute of TechnologyETHZ - ETLZurichSwitzerland

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