Tiêu đề EE 21_Lesson 4_Basic System Properties.pdf ✅

Feedback Control Systems Basic System Properties Engr. Lancer Andre T. Mendoza PRESENTED BY
Back to Agenda Basic System Properties Linearity (Linear System & non-linear system) Time Invariance (Time- invariant system & time-variant system) Memory (Static & dynamic system) Causality (causal system & non – causal system) Stability (stable system & unstable system) Invertibility (invertible system & non-invertible system)
Back to Agenda PRESENT, PAST, & FUTURE INPUTS Consider the following cases of system: i. y(t) = x(t) ii. y(t) = x(t − 1) iii. y(t) = x(t + 1) Take t = 0 or t = 1 or any value. Taking t = 0 for example, Present: t = 0 Past: t = −1 Future: t = +1 Thus, I. y(t) = x(t) II. y(t) = x(t − 1) III. y(t) = x(t + 1) y(0) = x(0) present output; present input y(0) = x(−1) present output; past input y(0) = x(+1) present output; future input
Back to Agenda LINEARITY A system S is linear if it has the additivity property and the homogeneity property. Let: y1 ≔ Sx1 and y2 ≔ Sx2. (:= means “is defined to be’) Additivity: y1 + y2 = s x1 + x2 Homogeneity: ay1 = S ax1 , ∀a ∈ C Homogeneity means that the response of S to the scaled signal ax1 is a times the response y1 = Sx1. An important consequence is that the response of linear system to the 0 signal is the 0 signal.