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]

External Links[edit | edit source]