Exams › GATE › Technical
The characteristic equation of a linear time-invariant (LTI) system is given by Δ(s)=s⁴+3s³+3s²+s+k=0. The system is BIBO stable if
- 0 < k < 12/9
- k > 3
- 0 < k < 8/9
- k > 6
Correct answer: 0 < k < 8/9
Solution
The correct option indicates that for the system to be BIBO stable, the roots of the characteristic equation must lie in the left half of the complex plane, which occurs when the coefficients of the polynomial satisfy certain conditions. The range 0 < k < 8/9 ensures that all roots have negative real parts, thus guaranteeing stability.
Related GATE Technical questions
- A system transfer function is H(s) = (a1s² + b1s + c1)/(a2s² + b2s + c2). If a1 = b1 = 0, and all other coefficients are positive, the transfer function represents a
- The symbols, a and T, represent positive quantities, and u(t) is the unit step function. Which one of the following impulse responses is NOT the output of a causal linear time-invariant system?
- A 5 kVA, 50 V/100 V, single-phase transformer has a secondary terminal voltage of 95 V when loaded. The regulation of the transformer is
- The parameter of an equivalent circuit of a three-phase induction motor affected by reducing the rms value of the supply voltage at the rated frequency is
- A three-phase synchronous motor draws 200 A from the line at unity power factor at rated load. Considering the same line voltage and load, the line current at a power factor of 0.5 leading is
- Given, Vgs is the gate-source voltage, Vds is the drain source voltage, and Vth is the threshold voltage of an enhancement type NMOS transistor, the conditions for transistor to be biased in saturation are
⚔️ Practice GATE Technical free + battle 1v1 →