The course provides a basic knowledge on formulation and computer implementation of dynamical system models. It starts from theoretical issues of Laplace and Z transform in their application to describing the continuous and discrete linear systems respectively. A particular emphasis is given on the skills in describing the dynamic processes in the state space approach in both linear and non-linear systems.

A) Laplace and Z transform
1. The basic properties of the Laplace transforms
2. L transform solution of Cauchy problem in differential equations, inverse L transform
3. Convolution integral transform and transfer function models
4. Fourier transform, Bode diagram of the linear model
5. The basic properties of the Z transform
6. Sampled data linear system, discrete transfer function
7. Z transform solution of the difference equation, inverse Z transform
B) State space model of dynamic system
10. The state space notion, state variables, state trajectory
11. Introduction methods of state variables, state equations
12. Steady state of the system, static characteristics, types of singular points
13. Characteristic function of the linear dynamic system, stability notion
C) Computer model
15. Methods of numerical solution of the state space equation
16. Sampling time assessment, stability of the numerical method
17. Explicit and implicit methods, predictor-corrector

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Ogata K.: Modern Control Engineering. Prentice-Hall, Inc. Englewood Cliffs, N. Jersey, 1990.
Zítek P.: Matematicke a simulační modely 1 a 2, ČVUT Praha, 2004.