Linear systems

Linear systems

• Linear systems
• Autonomous linear dynamical system
• Linearization near equilibrium point
• Solution via Laplace transform and matrix exponential
• Controllability & observability

 

Linear dynamical systems with inputs & outputs

• Recall continuous-time time-invariant LDS has form

 

 

• Ax is called the drift term
• Bu is called the input term

 

 

 

Example 

 

 

 

 

Controllability & observability

 

 

 

Modal decoupling