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LMIs in Control/Stability Analysis/Continuous Time/Transient Output Bound for Autonomous LTI Systems
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The System
Consider a continuous-time LTI system with a state-space representation of:
where , and ,
the transient bound on the output can be evaluated with the following LMI.
The Data
, and .
The LMI:
The Euclidean norm of the output satisfies
if there exists and , where , such that
Conclusion
By using this LMI the transient output bound can be found for a given autonomous LTI system.
Implementation
The LMI given above can be implemented and solved using a parser such as YALMIP, along with an LMI solver such as SeDuMi, or MOSEK. (For a detailed list of solvers, please visit this page on Relevant Solvers).
References
LMI Properties and Applications in Systems, Stability, and Control Theory Caverly Ryan 2021 Forbes James