(a) find the relationship between input u and output y when the system is at equilibrium. denote the equilibrium input/output pair (operating point) (ue, ye).
(b) find the linearized state-space representation of the above nonlinear system around the equilibrium pair (operating point) (ue, ye) and the associated transfer function. the respective representation will be parameterized by ue and ye.
(c) find the conditions on the equilibrium pair (operating point) (ue, ye), when the linearized system in (b) is unstable.