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

Introduction edit

Wile in the case of autonomous systems, they only need initial input constraints and cannot be changed using external inputs; the non-autonomous systems on the other hand can have changes happen to its behavior using a controller.

The System edit

Consider the discrete-time LTI system with state space realization
 
 

The Data edit

 ,  ,  ,  

Determining the bound edit

The output of this system must satisfy
 
if there exists some matrix  and scalar  , where  , such that
 ,

 .

Implementation edit

This can be implemented in any LMI solver such as YALMIP, using an algorithmic solver like Gurobi.

Conclusion edit

Given a non-autonomous system with initial operating conditions and a controller, the parameter   can be used to determine the feasible bound on the output of that system.

Related LMIs edit

External Links edit