1. EECE 396-1 Hybrid and Embedded Systems: Computation T. John Koo, Ph.D. Institute for Software Integrated Systems Department of Electrical Engineering and Computer Science Vanderbilt University 300 Featheringill Hall February 3, 2004 john.koo@vanderbilt.edu http://www.vuse.vanderbilt.edu/~kootj

2. 2 Hybrid System A system built from atomic discrete components and continuous components by parallel and serial composition, arbitrarily nested. The behaviors and interactions of components are governed by models of computation (MOCs). Discrete Components Finite State Machine (FSM) Discrete Event (DE) Synchronous Data Flow (SDF) Continuous Components Ordinary Differential Equation (ODE) Partial Differential Equation (PDE)

3. 3 Modeling:Ordinary Differential Equations

4. 4 Topics Ordinary Differential Equations Definitions Examples Existence and Uniqueness of Solutions Properties of Solutions Ref: [1] S. S. Sastry, Nonlinear Systems: Analysis, Stability, and Control, Springer, 1999. [2] J. J. Slotine and W. Li, Applied Nonlinear Control, Prentice Hall, 1991. [3] H. K. Khalil, Nonlinear Systems, Macmillan, 1992.

5. 5 Ordinary Differential Equations

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10. 10 Ordinary Differential Equations

11. 11 Ordinary Differential Equations

12. 12 Ordinary Differential Equations

13. 13 Ordinary Differential Equations

14. 14 Ordinary Differential Equations

15. 15 Ordinary Differential Equations

16. 16 Ordinary Differential Equations

17. 17 Ordinary Differential Equations

18. 18 End