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Consider the system xlt) = f(x(t)), y(t)=h(x(t)) for functions f:R">R" and h=R" → Rm Prove that the system is time invariant.

Consider the system xlt) = f(x(t)), y(t)=h(x(t)) for functions f:R">R" and h=R" → Rm Prove that the system is time invariant.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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Consider the system xlt) = f(x (t)), y(t) = h(x(t)) for functions f:R" →R" and h=R" → Rm Prove that the system is time invariant.
Transcribed Image Text:Consider the system xlt) = f(x (t)), y(t) = h(x(t)) for functions f:R" →R" and h=R" → Rm Prove that the system is time invariant.
Expert Solution
Step 1

                             SOLUTION

GIVEN-->

              x'(t) = f(x(t))

             y(t)  = h(x(t))

ASSUME-->

                   y(t) = OUTPUT

                   x(t) = INPUT

.FOR SYSTEM TO BE TIME INVARIANT

                   y(t) = y(t-T)

                 T = Time delay in Input & Output

 

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