Problem 3: Determine the stability of the DTS whose state equation is given as

 

 

Problem 4: Find out the equilibrium points of the following nonlinear system

 

Lecture Note 3

Exercise Problems:

Problem:1 Consider a non-linear system

 

Linearize the system about origin which is an equilibrium point.

Problem:2 Is the following function positive definite ?

 

Problem:3 Is the following matrix positive definite?

 

Problem:4 Consider the following matrices of order 3 and determine the sign definiteness of them.

 

Problem 5:

• (a) Consider a system whose system matrix is

 

Investigate the stability of the system using Lyapunov method.

• (b) Consider a system described by the linear time-invariant equation

 

Investigate the stability of the system using the Lyapunov method.