If the input x(t) and output y(t) of a system are related as y(t) = max(0, x(t)), then the system is

linear and time-variant
linear and time-invariant
non-linear and time-variant
non-linear and time-invariant

Correct answer: non-linear and time-invariant

Solution

The system is non-linear because it involves the maximum function, which does not satisfy the principle of superposition, and it is time-invariant since the output does not change if the input is shifted in time.

Related GATE Technical questions

Two discrete-time linear time-invariant systems have impulse responses h1[n] = δ[n−1] + δ[n+1] and h2[n] = δ[n−1] + δ[n+1], where δ[n] is the Kronecker delta. The overall system is
Consider a power system consisting of N number of buses. Buses in this power system are categorized into slack bus, PV buses and PQ buses for load flow study. The number of PQ buses is N_L. The balanced Newton-Raphson method is used to carry out load flow study in polar form. H, S, M, and R are sub-matrices of the Jacobian matrix J as shown below: [ΔP] [ΔQ] = J [Δδ] [ΔV], where J = [H S M R] The dimension of the sub-matrix M is
Inductance is measured by
In the Nyquist plot of the open-loop transfer function G(s)H(s) = (3s + 5)/(s - 1) corresponding to the feedback loop shown in the figure, the infinite semi-circular arc of the Nyquist contour in s-plane is mapped into a point at
Consider a unity-gain negative feedback system consisting of the plant G(s) (given below) and a proportional-integral controller. Let the proportional gain and integral gain be 3 and 1, respectively. For a unit step reference input, the final values of the controller output and the plant output, respectively, are G(s) = 1/(s - 1)
The following columns present various modes of induction machine operation and the ranges of slip A Mode of operation a. Running in generator mode b. Running in motor mode c. Plugging in motor mode B Range of Slip p) From 0.0 to 1.0 q) From 1.0 to 2.0 r) From -1.0 to 0.0 The correct matching between the elements in column A with those of column B is

⚔️ Practice GATE Technical free + battle 1v1 →