The Routh-Hurwitz stability criterion is a mathematical test that determines the stability of a linear time-invariant control system. It uses the characteristic polynomial of the system and constructs Hurwitz determinants to analyze the signs and determine if all roots of the polynomial have negative real parts, indicating stability. The document discusses the theorem, characteristic equation, determinant form, and references related to the Routh-Hurwitz stability criterion.

1. Routh hurwitz stability criterion
Mr. Somesh Chaturvedi Gurpreet Singh(K10966)
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2. INTRODUCTION
In control system theory, the Routh–Hurwitz
stability criterion is a mathematical test that is a
necessary and sufficient condition for the stability of
a linear time invariant (LTI) control system. The
Routh test is an efficient recursive algorithm that
English mathematician Edward John Routh
proposed in 1876 to determine whether all the roots
of the characteristic polynomial of a linear system
have negative real parts.

3. THEORAM
From the first equality we can for instance conclude that
when the variation of the argument of f(iy) is positive,
then f(z) will have more roots to the left of the imaginary
axis than to its right

4. CHARACTERSTIC EQ.
With the help of characteristic equation, we will
make a number of Hurwitz determinants in order to
find out the stability of the system. We define
characteristic equation of the system as

5. DETERMINANT FORM
 The value of this determinant is given by |a1| where a1 is the coefficient of sn-1
in
the characteristic equation. Determinant two : The value of this determinant is
given by
Here number of elements in each row is equal to determinant number and
we have determinant number here is two. The first row consists of first two
odd coefficients and second row consists of first two even coefficients.

6. DETERMINANT

7. REFERENCE
Baines, W. D. 1975 Entrainment by a plume or jet at
a density interface. J. Fluid Mech. 68, 309{320.
Baines, W. D. & Turner, J.S. 1969 Turbulent buoyant
convection in a source in a conffined region. J. Fluid
Mech. 37, 51.

ASHRAE. 1993. Handbook of Fundamentals,
American Society of Heating, Refrigerating, and Air
Conditioning Engineers, Inc., Atlanta.

8.  Thank you