(Solved): A CT-LTI system has the following transfer function: \[ H(s) \triangleq \frac ...

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A CT-LTI system has the following transfer function: \[ H(s) \triangleq \frac{Y}{X}(s)=\frac{s^{4}+2.3 s^{3}+3.4 s^{2}+2.3 s-1}{s^{4}+2.4 s^{3}+3.4 s^{2}+1.8 s+1} \] (a) Using the first canonical form, obtain a state-space representation (block diagram and state-equations, in matrix form) that describes the system. (b) Assume zero initial conditions, obtain the differential equation that describes that system. (c) Is the inverse of that system stable? Verify your answer. (d) Is the system causal? Verify your answer.