Step 1: Bode criterion.
In Bode stability analysis, stability margin is determined from the frequency response where both gain and phase generally decrease with frequency.
Step 2: Option check.
- (A) Correct: Applicable when both decrease.
- (B), (C), (D): Do not reflect the typical behavior required for Bode stability analysis.
Final Answer: \[ \boxed{\text{A) gain and phase curves both decrease with frequency}} \]
Given an open-loop transfer function \(GH = \frac{100}{s}(s+100)\) for a unity feedback system with a unit step input \(r(t)=u(t)\), determine the rise time \(t_r\).
Consider a linear time-invariant system represented by the state-space equation: \[ \dot{x} = \begin{bmatrix} a & b -a & 0 \end{bmatrix} x + \begin{bmatrix} 1 0 \end{bmatrix} u \] The closed-loop poles of the system are located at \(-2 \pm j3\). The value of the parameter \(b\) is: