LMIs in Control/Stability Analysis/Continuous Time/Output Energy Bound for Non-Autonomous LTI Systems
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Introduction[edit | edit source]
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 | edit source]
Consider the continuous-time LTI system with state space realization
The Data[edit | edit source]
, , , &
Determining the bound[edit | edit source]
The output of this system must satisfy
if there exists some matrix and scalar ,
where
,
such that
,
.
Implementation[edit | edit source]
This can be implemented in any LMI solver such as YALMIP, using an algorithmic solver like Gurobi.
Conclusion[edit | edit source]
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 | edit source]
- LMIs in Control/Stability Analysis/Discrete Time/Output Energy Bound for Autonomous LTI Systems
- LMIs in Control/Stability Analysis/Discrete Time/Output Energy Bound for Non-Autonomous LTI Systems