Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > Which of the following systems is stable?a)y(...
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Which of the following systems is stable?
- a)y(t) = log(x(t))
- b)y(t) = sin(x(t))
- c)y(t) = exp(x(t))
- d)y(t) = tx(t) + 1
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Which of the following systems is stable?a)y(t) = log(x(t))b)y(t) = si...
Stability implies that a bounded input should give a bounded output. In a,b,d there are regions of x, for which y reaches infinity/negative infinity. Thus the sin function always stays between -1 and 1, and is hence stable.
Most Upvoted Answer
Which of the following systems is stable?a)y(t) = log(x(t))b)y(t) = si...
Stability of Systems
Stability is an important property of any system, and it refers to the ability of the system to remain bounded and not diverge to infinity. A stable system is one that will always return to its equilibrium state after being subjected to a disturbance. There are different ways to classify the stability of a system, but the most common one is based on the concept of boundedness.
Types of Stability
There are three types of stability:
1. BIBO Stability (Bounded-Input Bounded-Output Stability): this type of stability ensures that if the input signal to the system is bounded, then the output signal must also be bounded.
2. Asymptotic Stability: this type of stability ensures that the system returns to its equilibrium state after being subjected to a disturbance.
3. Lyapunov Stability: this type of stability ensures that the system does not diverge to infinity.
Stability of the given systems
a) y(t) = log(x(t)): This system is not BIBO stable as the logarithmic function is unbounded. It can cause the output to become unbounded even if the input signal is bounded.
b) y(t) = sin(x(t)): This system is asymptotically stable as the sinusoidal function is bounded, and it will always return to its equilibrium state (zero) after being subjected to a disturbance.
c) y(t) = exp(x(t)): This system is not BIBO stable as the exponential function is unbounded. It can cause the output to become unbounded even if the input signal is bounded.
d) y(t) = tx(t): This system is not BIBO stable as the output can become unbounded if the input signal is unbounded.
Conclusion
The only stable system among the given options is y(t) = sin(x(t)) as it is asymptotically stable. The other systems are not stable as they can cause the output to become unbounded even if the input signal is bounded.
Stability is an important property of any system, and it refers to the ability of the system to remain bounded and not diverge to infinity. A stable system is one that will always return to its equilibrium state after being subjected to a disturbance. There are different ways to classify the stability of a system, but the most common one is based on the concept of boundedness.
Types of Stability
There are three types of stability:
1. BIBO Stability (Bounded-Input Bounded-Output Stability): this type of stability ensures that if the input signal to the system is bounded, then the output signal must also be bounded.
2. Asymptotic Stability: this type of stability ensures that the system returns to its equilibrium state after being subjected to a disturbance.
3. Lyapunov Stability: this type of stability ensures that the system does not diverge to infinity.
Stability of the given systems
a) y(t) = log(x(t)): This system is not BIBO stable as the logarithmic function is unbounded. It can cause the output to become unbounded even if the input signal is bounded.
b) y(t) = sin(x(t)): This system is asymptotically stable as the sinusoidal function is bounded, and it will always return to its equilibrium state (zero) after being subjected to a disturbance.
c) y(t) = exp(x(t)): This system is not BIBO stable as the exponential function is unbounded. It can cause the output to become unbounded even if the input signal is bounded.
d) y(t) = tx(t): This system is not BIBO stable as the output can become unbounded if the input signal is unbounded.
Conclusion
The only stable system among the given options is y(t) = sin(x(t)) as it is asymptotically stable. The other systems are not stable as they can cause the output to become unbounded even if the input signal is bounded.
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Which of the following systems is stable?a)y(t) = log(x(t))b)y(t) = sin(x(t))c)y(t) = exp(x(t))d)y(t) = tx(t) + 1Correct answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Which of the following systems is stable?a)y(t) = log(x(t))b)y(t) = sin(x(t))c)y(t) = exp(x(t))d)y(t) = tx(t) + 1Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following systems is stable?a)y(t) = log(x(t))b)y(t) = sin(x(t))c)y(t) = exp(x(t))d)y(t) = tx(t) + 1Correct answer is option 'B'. Can you explain this answer?.
Which of the following systems is stable?a)y(t) = log(x(t))b)y(t) = sin(x(t))c)y(t) = exp(x(t))d)y(t) = tx(t) + 1Correct answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Which of the following systems is stable?a)y(t) = log(x(t))b)y(t) = sin(x(t))c)y(t) = exp(x(t))d)y(t) = tx(t) + 1Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following systems is stable?a)y(t) = log(x(t))b)y(t) = sin(x(t))c)y(t) = exp(x(t))d)y(t) = tx(t) + 1Correct answer is option 'B'. Can you explain this answer?.
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