LMIs in Control/Stability Analysis/Discrete Time/Transient Bound for Discrete-Time Non-Autonomous LTI Systems

The System edit

For a discrete-time LTI system with a state-space representation of:

 

where  , and  ,

the transient bound can be analyzed with the LMI below.

The Data edit

 , and  

The LMI: edit

The Euclidean norm of the state satisfies:

 

if there exists some   and  , where P > 0 such that:

  •  
  •  
  •  

if x0 = 0 and u is a unit-energy input ( ), then the above LMIs ensure that  

Conclusion edit

By using this LMI the transient state bound can be analyzed for a given non-autonomous LTI system.

Implementation edit

The LMI given above can be implemented and solved using a tool such as YALMIP, along with an LMI solver such as MOSEK.

Related LMIs edit

External Links edit