Abstract
The digital character of computers incites us now to turn the spotlight onto sampled control systems, where the control is fed into the system only at discrete times. In § 6.2, we describe how a continuous-time linear dynamical system can be sampled, yielding an exact discretized discretetime linear dynamical system. Then, we investigate the stability of discrete-time classical dynamical systems in § 6.3, and that of controlled discrete-time linear dynamical systems in § 6.4. Controllability and regulator design are tackled in § 6.5, observability and observer design in § 6.6, making it possible to focus on observer-regulator synthesis and on the separation principle in § 6.7. The choice of the sampling period is discussed in § 6.8. The links between controlled discrete-time linear dynamical systems and the input-output representation are the subject of § 6.9. Finally, we show how a control law in discrete-time can locally stabilize a nonlinear continuous-time dynamical system in § 6.10.
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