Routh-Hurwitz and Various Plots

By : Vandana Tanwar

Updated : Feb 3, 2021, 9:15

Routh-Hurwitz and Various Plots study material for GATE ECE explains the practical uses of these concepts for finding the stability of a system. You will also study in Routh-Hurwitz, and Various Plots GATE notes that a system is stable if every root of the characteristic equation lies on the right-half side of the s-plane. Similarly, Routh-Hurwitz and Various Plots notes for ECE mention that a system is marginally stable if all the system’s roots lie on the S-plane’s imaginary axis. The criteria is the primary topic of importance in Routh-Hurwitz and Various Plots syllabus for GATE. This criterion says that a system is only stable if every root in the first column has the same sign. Even if they don’t have the same sign, the number of sign changes in the first column should be equal to the equation’s roots in the s-plane’s right half. You could be asked questions relating to such concepts in any Routh-Hurwitz and Various Plots online test. 

Important Routh-Hurwitz and Various Plots Topics for GATE ECE

Here are the important topics for Routh-Hurwitz and Various Plots for GATE ECE.



Relative Stability Analysis

For examining the relative stability of a system, shift the s-plane by substituting s = z - (alpha) in the characteristic equation. Here alpha is constant. 

Jury Stability Test

This test determines if the roots of a polynomial lie within a unit circle. You can apply this stability test without solving the characteristic equation for roots. 

Root Locus Technique 

The root locus technique is used for predicting the behaviour of a closed-loop system after a parameter of the same system has been changed. Typically, the gain of the system is changed when the root-locus technique is applied. 

Bode Plot

Bode Plot determines the stability of a control system using a graphical method. It is based on sinusoidal frequency response. 

Other Topics

Minimum phase transfer function, non-minimum phase, and all-pass transfer functions. 

Tips To Solve Routh-Hurwitz and Various Plots Questions for GATE ECE

  • The study from Routh-Hurwitz and Various Plots notes for GATE PDF is essential. These notes will help you in remembering the vital points in the main exam. 
  • Questions of Routh-Hurwitz and Various Plots for computer science and other engineering branches are mostly graphical. Thus, you must spend your maximum time-solving Routh-Hurwitz and Various Plots GATE questions by looking at Routh-Hurwitz and Various Plots GATE questions and answering PDF for correcting your mistakes. 
  • When you take a quiz, always check that it is based on the current Routh-Hurwitz and Various Plots GATE syllabus. If it isn’t you’d surely be disappointed to find out of syllabus questions in it. 

Importance of Routh-Hurwitz and Various Plots for GATE ECE

  • Routh-Hurwitz and Various Plots are a part of Control Systems that are used to design any stable system. 
  • Nearly three questions are asked based on this topic for GATE exams. 
  • The average weightage of Routh-Hurwitz and Various plots in GATE is 1.5 marks. 
  • It deals with the logical and analytical skills of the candidate during the exam.

Most Recommended Routh-Hurwitz and Various Plots Books for GATE ECE

In addition to solving the Routh-Hurwitz and Various Plots quiz and studying from notes, you can refer to these books for scoring better marks in GATE. Experts have recommended learning from these vital subject books. 



Automatic Control Systems 

Benjamin Kuo

Control System Engineering 

M. Gopal 

Control Systems Engineering

Norman Nise

Why prepare Routh-Hurwitz and Various Plots from BYJU'S Exam Prep?  

GATE exams are among the most important ways to get into the postgraduate programs at IITs and IISc. The students clearing this exam could also get placed as government officers in different places like ONGC. BYJU'S Exam Prep knows the tips and tricks required for succeeding in the main exams. It provides a detailed study of every topic through elaborate video lessons that are selectively available for every user that creates a free account on the website. You can access unlimited Routh-Hurwitz and Various Plots MCQ PDF and Routh-Hurwitz and Various Plots online quiz here.

Frequently Asked Questions (FAQs): 

Q. What is the Routh Hurwitz criterion used for? 

The Routh Hurwitz criterion is used to get the number of roots in the s-plane’s right half. 

Q. Where can Routh Hurwitz criterion not be applied? 

We cannot apply the Routh Hurwitz criterion where the system’s characteristic equation containing coefficients is the sinusoidal, exponential, and complex functions of the s-plane. 

Q. Does stability analysis utilise which test signal in the best way? 

Stability analysis utilises Impulse signal in the best way. It reduces the computational task to a greater extent. 

Q. What is the necessary condition for the stability of a linear system? 

The necessary condition for the stability of a linear system is that for the characteristic equation G(s)H(s) + 1 = 0, every coefficient must be real, and they must have the same sign. 

Q. What should you do to make an unstable system stable? 

You must decrease the gain of the system for making an unstable system stable. 

Q. In the G planes, all the constant N-circles cross the real axis at points that are fixed. These points are: 

For this sum, the centre of the N-circle is (-1/2, 1/2N). Thus, N =tanα. Always, (-1,0) and (0,0) are the points through which N-circles pass.