In this part, there are three systems provided as follows system E: y(t) + 9ty(t) = 9u(t + 1) system G: y(t) + 7y(t) + 12y(t) = u(t) system K: 8y2(t) + 3e(t) = t sin(u(t)) The time t in all systems and signals, including input u(t) and output y(t), are only considered in the range t > 0. Answer the following questions. 1. [12%] Classify each one of the systems as linear or non-linear, time-variant or time-invariant, causal or non-causal, static or dynamic. system E system G system K linearity time dependency causality static/dynamic 2. [9%] Rewrite the system G in the state space format. Define the state vector x(t), and find the matrices A, B, and C in the state dynamics x = Ax+ Bu y = Cx ference input for the closed loop system and R(s) is the Laplace Transform of rit) (a) and determine whether the system Ga(s) is BIBO stable and who stable. 3. [4%] Following question 2, write the Laplace Transform of the state dynamic equation in the following form Y(s) = H(s, x(0)) + G(s)U(s) where x(0) is the initial condition of the system, U(s) and Y(s) are the Laplace Transform of u(t) and y(t), respectively. Find the free response H(s, x(0)) and the transfer function G(s) together with the poles of the system.