A nonlinear system is described by the following eq'uations, XI = 2xi + 3xi - 2xz + u

±z = xz - 0.25(sin XI +cos x2) + u.

(a) With u = 0 plot the state-space trajectories in the neighborhood of the origin defined by lxii ~ 1, lxzl ~ 2.

(b) Using Lyapunov's first method, linearize the above system about XI =

x2 = u = 0, and assess the stability of this linearized system.

Problem