The document discusses the stability of control systems, categorizing stability into stable, unstable, and marginally stable systems. It explains several types of stability criteria including BIBO, asymptotic, absolute, relative, and conditional stability, with emphasis on the Routh-Hurwitz criterion for analyzing stability. Limitations of the Hurwitz criterion are also outlined, emphasizing its complexity in practical applications.

1. Stability of a
Control System
Topic:

2. CONTENTS
01 I n t r o d u c t i o n
03
H u r w i t z a n d
R o u t h S t a b i l i t y
c r i t e r i o n
02 C o n c e p t o f
S t a b i l i t y
04 C o n c l u s i o n

3. Stability means whether the system is
stable or unstable.
Stability is of three types :
• Stable system
• Unstable system
• Marginally stable system

4. Types of System
• Stable system: The system is said to be stable when only the output is
bounded for bounded input.
• Unstable system: For a bounded input the output is unbounded in the
system.
• Marginally stable system: If given an impulse of infinite magnitude as
input and given unbounded output, but neither will the output return to
zero.

5. Stability of a Control System can be classified into 5 chategories:
• BIBO(Bounded Input Bounded Output): Output should be bounded
for bounded input.
• Asymptotic Stability(Zero stability): There will be zero output for zero
input.
• Absolute Stability: For a bounded input, the system is stable for all the
values of system parameters.
• Relative Stability: It indicates how close the system is to instability.
• Conditional Stability: Stability of a system for a particular range of any
or some parameters.

6. • If all the coefficient of characterstics equation may lie on the LHS of s-plane.
• This is necessary but not sufficient condition to ensure the stability of closed loop
system or to ensure that roots of characterstics equation are on the left hand side of
s-plane for that we propose Routh Table or Routh Array.
• The characterstics equation of the nth order continuous system can be written as:
• The stability criterion is applies using
a Routh table which is defined as:
Routh Hurwitz Criteria
• Where an, an-1 ,....a0 are coefficients
of the characterstics equation.

7. Limitations of Hurwitz Criterion
1. Very time consuming and combursion technique to solve large
determinants for higher order systems.
2. It doesn't tell the exact no. of Right half poles.
3. Determinants of marginal stability becomes tough using this method.

8. Conclusion
• So from the above ppt we were able
to know about the basics of stability
and also the cocept of stability.
• The verification of stability using the
Routh Hurwitz criteria helps us to
know if a sysytem is stable or not, so
in practice it is desired to follow
Relative stability.

9. • Class notes
• Control System- Stability Tutorials
• Slideshare-Circuit network analysis- Chapter 5
Reference

10. THANKYOU
Submitted By:
Sonali Baral
1804614@kiit.ac.in