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Time Domain Analysis of Linear Systems Ch2

Time Domain Analysis of Linear Systems Ch2. University of Central Oklahoma Dr. Mohamed Bingabr. Outline. Zero-input Response Impulse Response h(t) Convolution Zero-State Response System Stability. Time Domain Analysis. Zero-State Response. If M = N then

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Time Domain Analysis of Linear Systems Ch2

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  1. Time Domain Analysis of Linear SystemsCh2 University of Central Oklahoma Dr. Mohamed Bingabr

  2. Outline • Zero-input Response • Impulse Response h(t) • Convolution • Zero-State Response • System Stability

  3. Time Domain Analysis Zero-State Response

  4. If M = N then h(t) = b0(t)+ [P(D) yn(t)] u(t)

  5. n n

  6. n

  7. n n

  8. n

  9. HW3_Ch2: 2.2-1, 2.2-4, 2.2-6, 2.3-1, 2.3-4, 2.4-5, 2.4-8

  10. Example Find the total response for the system D2y + 3Dy + 2y = Dx for input x(t)=10e-3tu(t) with initial condition y(0) = 0 and Answer For t  0 Zero-input Response Zero-state Response Natural Response Forced Response

  11. System Stability • External Stability (BIBO) • If the input is bounded then the output is bounded • . • Internal Stability (Asymptotic) • If and only if all the characteristic roots are in the LHP • Unstable if, and only if, one or both of the following conditions exist: • At least one root is in the RHP • There are repeated roots on the imaginary axis • Marginally stable if, and only if, there are no roots in the RHP, and there are some unrepeated roots on the imaginary axis.

  12. Example Investigate the asymptotic & BIBO stability of the following systems: • (D+1)(D2 + 4D + 8) y(t) = (D - 3) x(t) • (D-1)(D2 + 4D + 8) y(t) = (D + 2) x(t) • (D+2)(D2 + 4) y(t) = (D2+ D + 1) x(t) HW4_Ch2: 2.4-18 (pair d), 2.4-20, 2.4-23, 2.4-33, 2.6-1

  13. Signals Demonstrations http://www.jhu.edu/~signals/

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