The characteristic equation for the system is \[ s^3 + 9s^2 + 26s + 12(2 + K_c) = 0 \] Using Routh test, the value of Kc that will keep the system stable is:

Question

If the number of zeros is less than the number of poles, i.e. \( Z<P \), then the value of the transfer function becomes zero for \( s \to \infty \). Hence, some zeros are located at infinity and the order of such zeros will be:

Answer 1

Step 1: Routh-Hurwitz Criterion Application.
The Routh-Hurwitz criterion is utilized to assess system stability. The Routh array is constructed from the characteristic equation's coefficients. For stability, the number of sign changes in the first column indicates the \(K_c\) value that ensures system stability.

Step 2: Conclusion.
Based on the Routh test, the system remains stable with a \(K_c\) value of (C) 13.5.

Firm 2	Cooperate	Compete
Firm 1	5, 5	0, 10
Compete	10,0	2, 2

The characteristic equation for the system is \[ s^3 + 9s^2 + 26s + 12(2 + K_c) = 0 \] Using Routh test, the value of Kc that will keep the system stable is:

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The Correct Option is C

Solution and Explanation

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