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##### SHORT QUESTIONS AND ANSWERS

Q1. Define the following:

(i) zero input response (ii) zero state response (iii) characteristic polynomial (iv) characteristic equation and (v) eigen values

Ans.:

(i) Zero Input Response (ZIR): The response which occurs even without input is known as zero input response and it is due to initial condition.

ZIR = Φ(k) x(0) = Ak x(0)

where           Φ(k) = A kis termed as the state transition matrix.

(ii) Zero State Response: The response which occurs when all initial conditions are zero is known as zero state response. (iii) Characteristic Polynomial: The characteristic polynomial of the matrix A of order

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