1. Explain the concept of Lyapunov's stability theorem. How is Lyapunov function for a system determined?

2. Determine the stability of the system X where A
1

by Lyapunov's theorem and hence determine a Lyapunov function for the system.

3. A system is described by the following state space model:

1 0
0 0 1 0 u
0 x

Design a state feedback controller such that the closed loop poles are placed at ± j and -5.

4. Find Z transform of the discrete ramp function

k,k
0,k 0.

5. Explain non-linear system linearization methods in detail.

6. Construct the state model of the following electrical system

<img src='./qimages/15591-6.jpg'>

7. Explain the Genetic Algorithm application in adaptive control system with suitable examples.

8. A system is described by transfer function
6s^2 11s 6.
Find the state and output equation in matrix form and also test the controllability and observability of the system.

9. Write down the general form of "steady state Riccati-equation". How are these equations important? How do we solve these equations?

10. Write short notes on any two of the following:

Pontryagin's Maximum-Minimum Principle

Constrained Optimization

Describing function and its applications