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Consider the following statements related to Routh-Hurwitz criterion of determining the stability of a system:
1. It is applicable if the characteristic equation has real coefficients, complex ternrivS or exponential functions of s.
2. The criterion can be applied to any stability boundaries in complex plane, such as the unit circle in the z-plane.
3. The number of changes of signs in the elements of the first column equals the number of roots with negative real parts.
Which of these statements is/are not correct?
1. It is applicable if the characteristic equation has real coefficients, complex ternrivS or exponential functions of s.
2. The criterion can be applied to any stability boundaries in complex plane, such as the unit circle in the z-plane.
3. The number of changes of signs in the elements of the first column equals the number of roots with negative real parts.
Which of these statements is/are not correct?
- a)2 and 3 oniy .
- b)1, 2 and 3
- c)1 only
- d)1 and 2 only
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Consider the following statements related to Routh-Hurwitz criterion o...
• Routh-Hurwitz criterion is not applicable if characteristic equation has coefficients which are exponential or complex.
• It is not applied in z-piane because z-piane having unit circle is the stability boundary of discrete-data system.
• Statement-3 is also false because no. of sign change in 1st column of Routh’s array indicates the number of roots with positive real part or roots lying in RH s-plane.
• It is not applied in z-piane because z-piane having unit circle is the stability boundary of discrete-data system.
• Statement-3 is also false because no. of sign change in 1st column of Routh’s array indicates the number of roots with positive real part or roots lying in RH s-plane.
Most Upvoted Answer
Consider the following statements related to Routh-Hurwitz criterion o...
Statement 1: It is applicable if the characteristic equation has real coefficients, complex ternrivS or exponential functions of s.
This statement is correct. The Routh-Hurwitz criterion is a method used to determine the stability of a system based on the coefficients of the characteristic equation. It can be applied to systems with real coefficients, complex terms, or exponential functions of s.
Statement 2: The criterion can be applied to any stability boundaries in complex plane, such as the unit circle in the z-plane.
This statement is incorrect. The Routh-Hurwitz criterion is specifically applicable to continuous-time systems represented in the Laplace domain, not discrete-time systems represented in the z-domain. The unit circle in the z-plane is a stability boundary for discrete-time systems, and a different criterion, such as the Jury stability criterion, should be used to determine stability in the z-domain.
Statement 3: The number of changes of signs in the elements of the first column equals the number of roots with negative real parts.
This statement is correct. According to the Routh-Hurwitz criterion, if the number of sign changes in the first column of the Routh array is equal to the number of roots with negative real parts, then the system is stable. If there are any sign changes in the first column, it indicates the presence of roots with positive real parts, which implies instability.
Conclusion:
Based on the analysis of the statements, it can be concluded that Statement 2 is incorrect, while Statements 1 and 3 are correct. Therefore, option 'B' is the correct answer.
This statement is correct. The Routh-Hurwitz criterion is a method used to determine the stability of a system based on the coefficients of the characteristic equation. It can be applied to systems with real coefficients, complex terms, or exponential functions of s.
Statement 2: The criterion can be applied to any stability boundaries in complex plane, such as the unit circle in the z-plane.
This statement is incorrect. The Routh-Hurwitz criterion is specifically applicable to continuous-time systems represented in the Laplace domain, not discrete-time systems represented in the z-domain. The unit circle in the z-plane is a stability boundary for discrete-time systems, and a different criterion, such as the Jury stability criterion, should be used to determine stability in the z-domain.
Statement 3: The number of changes of signs in the elements of the first column equals the number of roots with negative real parts.
This statement is correct. According to the Routh-Hurwitz criterion, if the number of sign changes in the first column of the Routh array is equal to the number of roots with negative real parts, then the system is stable. If there are any sign changes in the first column, it indicates the presence of roots with positive real parts, which implies instability.
Conclusion:
Based on the analysis of the statements, it can be concluded that Statement 2 is incorrect, while Statements 1 and 3 are correct. Therefore, option 'B' is the correct answer.
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Consider the following statements related to Routh-Hurwitz criterion of determining the stability of a system:1. It is applicable if the characteristic equation has real coefficients, complex ternrivS or exponential functions of s.2. The criterion can be applied to any stability boundaries in complex plane, such as the unit circle in the z-plane.3. The number of changes of signs in the elements of the first column equals the number of roots with negative real parts.Which of these statements is/are not correct?a)2 and 3 oniy . b)1, 2 and 3c)1 only d)1 and 2 onlyCorrect answer is option 'B'. Can you explain this answer?
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Consider the following statements related to Routh-Hurwitz criterion of determining the stability of a system:1. It is applicable if the characteristic equation has real coefficients, complex ternrivS or exponential functions of s.2. The criterion can be applied to any stability boundaries in complex plane, such as the unit circle in the z-plane.3. The number of changes of signs in the elements of the first column equals the number of roots with negative real parts.Which of these statements is/are not correct?a)2 and 3 oniy . b)1, 2 and 3c)1 only d)1 and 2 onlyCorrect answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Consider the following statements related to Routh-Hurwitz criterion of determining the stability of a system:1. It is applicable if the characteristic equation has real coefficients, complex ternrivS or exponential functions of s.2. The criterion can be applied to any stability boundaries in complex plane, such as the unit circle in the z-plane.3. The number of changes of signs in the elements of the first column equals the number of roots with negative real parts.Which of these statements is/are not correct?a)2 and 3 oniy . b)1, 2 and 3c)1 only d)1 and 2 onlyCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements related to Routh-Hurwitz criterion of determining the stability of a system:1. It is applicable if the characteristic equation has real coefficients, complex ternrivS or exponential functions of s.2. The criterion can be applied to any stability boundaries in complex plane, such as the unit circle in the z-plane.3. The number of changes of signs in the elements of the first column equals the number of roots with negative real parts.Which of these statements is/are not correct?a)2 and 3 oniy . b)1, 2 and 3c)1 only d)1 and 2 onlyCorrect answer is option 'B'. Can you explain this answer?.
Consider the following statements related to Routh-Hurwitz criterion of determining the stability of a system:1. It is applicable if the characteristic equation has real coefficients, complex ternrivS or exponential functions of s.2. The criterion can be applied to any stability boundaries in complex plane, such as the unit circle in the z-plane.3. The number of changes of signs in the elements of the first column equals the number of roots with negative real parts.Which of these statements is/are not correct?a)2 and 3 oniy . b)1, 2 and 3c)1 only d)1 and 2 onlyCorrect answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Consider the following statements related to Routh-Hurwitz criterion of determining the stability of a system:1. It is applicable if the characteristic equation has real coefficients, complex ternrivS or exponential functions of s.2. The criterion can be applied to any stability boundaries in complex plane, such as the unit circle in the z-plane.3. The number of changes of signs in the elements of the first column equals the number of roots with negative real parts.Which of these statements is/are not correct?a)2 and 3 oniy . b)1, 2 and 3c)1 only d)1 and 2 onlyCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements related to Routh-Hurwitz criterion of determining the stability of a system:1. It is applicable if the characteristic equation has real coefficients, complex ternrivS or exponential functions of s.2. The criterion can be applied to any stability boundaries in complex plane, such as the unit circle in the z-plane.3. The number of changes of signs in the elements of the first column equals the number of roots with negative real parts.Which of these statements is/are not correct?a)2 and 3 oniy . b)1, 2 and 3c)1 only d)1 and 2 onlyCorrect answer is option 'B'. Can you explain this answer?.
Solutions for Consider the following statements related to Routh-Hurwitz criterion of determining the stability of a system:1. It is applicable if the characteristic equation has real coefficients, complex ternrivS or exponential functions of s.2. The criterion can be applied to any stability boundaries in complex plane, such as the unit circle in the z-plane.3. The number of changes of signs in the elements of the first column equals the number of roots with negative real parts.Which of these statements is/are not correct?a)2 and 3 oniy . b)1, 2 and 3c)1 only d)1 and 2 onlyCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
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Consider the following statements related to Routh-Hurwitz criterion of determining the stability of a system:1. It is applicable if the characteristic equation has real coefficients, complex ternrivS or exponential functions of s.2. The criterion can be applied to any stability boundaries in complex plane, such as the unit circle in the z-plane.3. The number of changes of signs in the elements of the first column equals the number of roots with negative real parts.Which of these statements is/are not correct?a)2 and 3 oniy . b)1, 2 and 3c)1 only d)1 and 2 onlyCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Consider the following statements related to Routh-Hurwitz criterion of determining the stability of a system:1. It is applicable if the characteristic equation has real coefficients, complex ternrivS or exponential functions of s.2. The criterion can be applied to any stability boundaries in complex plane, such as the unit circle in the z-plane.3. The number of changes of signs in the elements of the first column equals the number of roots with negative real parts.Which of these statements is/are not correct?a)2 and 3 oniy . b)1, 2 and 3c)1 only d)1 and 2 onlyCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Consider the following statements related to Routh-Hurwitz criterion of determining the stability of a system:1. It is applicable if the characteristic equation has real coefficients, complex ternrivS or exponential functions of s.2. The criterion can be applied to any stability boundaries in complex plane, such as the unit circle in the z-plane.3. The number of changes of signs in the elements of the first column equals the number of roots with negative real parts.Which of these statements is/are not correct?a)2 and 3 oniy . b)1, 2 and 3c)1 only d)1 and 2 onlyCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider the following statements related to Routh-Hurwitz criterion of determining the stability of a system:1. It is applicable if the characteristic equation has real coefficients, complex ternrivS or exponential functions of s.2. The criterion can be applied to any stability boundaries in complex plane, such as the unit circle in the z-plane.3. The number of changes of signs in the elements of the first column equals the number of roots with negative real parts.Which of these statements is/are not correct?a)2 and 3 oniy . b)1, 2 and 3c)1 only d)1 and 2 onlyCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Electrical Engineering (EE) tests.
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