Consider a system defined in state-space by \frac{\mathrm{dx}(t)}{\mathrm{d} t}=\mathbf{A x}(t)+\mathbf{B} u(t) y(t)=\mathbf{C x}(t)+\mathbf{D} u(t) \mathbf{A}=\left[\begin{array}{ll} 3 & 2 \\ 2 & 0 \end{array}\right], \quad \mathbf{B}=\left[\begin{array}{l} 4 \\ 2 \end{array}\right], \quad \mathbf{C}=\left[\begin{array}{ll} 2 & 0 \end{array}\right], \text { and } \mathbf{D}=0 Obtain the transfer function G(s) of the system. Show that the states of this system are not controllable. Carry out an observability test and design a state observer for this system. Place the observer poles at -5 rad/s and -10 rad/s. O Draw the block diagram of the state-space representation given by Equation (1). In terms of bounded-input bounded-output (BIB0) stability, when is a dynamic system stable? Classify poles and zeros according to their location in the s-plane.

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Consider a system defined in state-space by \frac{\mathrm{dx}(t)}{\mathrm{d} t}=\mathbf{A x}(t)+\mathbf{B} u(t) y(t)=\mathbf{C x}(t)+\mathbf{D} u(t) \mathbf{A}=\left[\begin{array}{ll} 3 & 2 \\ 2 & 0 \end{array}\right], \quad \mathbf{B}=\left[\begin{array}{l} 4 \\ 2 \end{array}\right], \quad \mathbf{C}=\left[\begin{arr