So according to the 2nd method of Lyapunov, the origin is not asymptotically stable. But it is stable. Remind the definition. B3) Propose a controller that renders the origin asymptotically stable. Lets choose k>0, that makes the system asymptotically stable. The system can then be interpreted as dissipative. Further reading: the problems 35 to 38 suggested in the notes on Optimal Control - State Space pp. 292-293. Representation - Modeling and Analysis, by Professor Sá da Costa, Check the examples of chapter 13 of Moder Control Engineering, by K. Ogata.
So according to the 2nd method of Lyapunov, the origin is not asymptotically stable. But it is stable. Remind the definition. B3) Propose a controller that renders the origin asymptotically stable. Lets choose k>0, that makes the system asymptotically stable. The system can then be interpreted as dissipative. Further reading: the problems 35 to 38 suggested in the notes on Optimal Control - State Space Representation - Modeling and Analysis, by Professor Sá da Costa, pp. 292-293. Check the examples of chapter 13 of Moder Control Engineering, by K. Ogata.
S6_sols.docx