Robust and Adaptive Control by Eugene Lavretsky & Kevin A. Wise

Author:Eugene Lavretsky & Kevin A. Wise
Language: eng
Format: epub
Publisher: Springer London, London

has the discontinuous (at the origin) right-half side, which is defined by the sign function

The system phase portrait is easy to draw and is given in Fig. 8.2.

Fig. 8.2Phase portrait of the system dynamics in Example 8.1

These data indicate that the system trajectories asymptotically approach either 1 or −1, depending on whether the initial conditions are negative or positive, respectively. The rate of change of the “kinetic energy” for this system is nonpositive:

Therefore, the kinetic energy must dissipate, and so it seems that the system trajectories should asymptotically approach the origin, where by the definition. To further investigate the system behavior, we can integrate the system dynamics on the interval from to :

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