Problems: (1) Answer True or False to each of the following. You must substantiate your answers. (A) A differentiable function is always globally Lipschitz. (B) The trajectory of the system , r(0) is...
Problems: (1) Answer True or False to each of the following. You must substantiate your answers. (A) A differentiable function is always globally Lipschitz. (B) The trajectory of the system , r(0) is bounded for all t 0 (C) A linear tine-varying system á(t) A(t)a(t) is asymptotically stable around the origin if and only if it is uniformly exponentially stable around the origin. (D) Given the equation x f(x), and suppose that xe 0 is an exponentially stable equilibrium point of the system. Then it must be the case that Df(ze) is Hurwitz.
Problems: (1) Answer True or False to each of the following. You must substantiate your answers. (A) A differentiable function is always globally Lipschitz. (B) The trajectory of the system , r(0) is bounded for all t 0 (C) A linear tine-varying system á(t) A(t)a(t) is asymptotically stable around the origin if and only if it is uniformly exponentially stable around the origin. (D) Given the equation x f(x), and suppose that xe 0 is an exponentially stable equilibrium point of the system. Then it must be the case that Df(ze) is Hurwitz.