LMIs in Control/Stability Analysis/Discrete Time/Transient Impulse Response Bound

The System

edit

Consider the single-input multi-output discrete-time LTI system with state-space realization
 ,
 

The Data

edit

 ,  , and  , and it is assumed that   is invertible. Let  . be the unit impulse response of the system. The Euclidian Norm of the impulse response satisfies the following LMI.

The LMI

edit

 

if there exist   and   where  , such that

 

 

and  


Implementation

edit

This can be implemented in any LMI parser such as YALMIP which can implement a solver like Mosek to return a solution.

Conclusion

edit

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

edit

References

edit

Caverly, Ryan; Forbes, James (2021). LMI Properties and Applications in Systems, Stability, and Control Theory.