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.