Basic Solution Matrices and Solution of Linear System

  Every system that make up by matrices has the reflection in the real world . We can describe a system in two differernt ways ; one is state space aspect ,the other is math aspect .The latter one we can only see the behavier of system ,the first one we can see more characters into this system . each system has three conditions .If we want to control the system ,we must know these deeply.

   Let's see it step by step.
  
   state space :
   1 numericual method

we can solve this system by matlab ,it is quite easy .

   Or we can do it in analytical way ,but this way is more complex than numeriual way .Because it must be calculated first ,get the result ,then you can simlink it by MATLAB .

 

     
See ,it is much complicated .

Also there are three results of roots : differernt roots ,the same roots and complex roots .But the method to solve them are the same .

In the space state ,we can see the controllability and observability in the system .

If the ans equals order ,it controllability  ,or uncontrollability.

The other way to describe the same system is in math ,it can be like

And there are two ways to slove it by MATLAB

numerical :

analytical(we should use math knowledge to solve it before):

This is the whole basic idea to do with linear Control system .We should know these 100 percent to keep on in deep study .