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LMIs in Control/Stability Analysis/Continuous Time/Transient State Bound for Non-Autonomous LTI Systems
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The System
For a continuous-time LTI system with a state-space representation of:
where , and x(0) = x0,
the transient bound can be evaluated with the following LMI.
The Data
, and x(0) = x0.
The LMI:
The Euclidean norm of the state satisfies:
if there exists and , where P > 0, such that:
if x0 = 0 and u is a unit-energy input (), then the above LMIs ensure that
Conclusion
By using this LMI the transient state bound can be analyzed for a given non-autonomous LTI system.
Implementation
The LMI given above can be implemented and solved using a tool such as YALMIP, along with an LMI solver such as MOSEK.
Related LMIs
Output Energy Bound for Autonomous LTI Systems
External Links
LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.