LMIs in Control/Click here to continue/LMIs in system and stability Theory/Transient State Bound for Non-Autonomous LTI Systems
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The System
[edit | edit source]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
[edit | edit source], and x(0) = x0.
The LMI:
[edit | edit source]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
[edit | edit source]By using this LMI the transient state bound can be analyzed for a given non-autonomous LTI system.
Implementation
[edit | edit source]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
[edit | edit source]External Links
[edit | edit source]- LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.