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LMIs in Control/Click here to continue/LMIs in system and stability Theory/Transient Bound for Discrete-Time Non-Autonomous LTI Systems
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The System
For a discrete-time LTI system with a state-space representation of:
where , and ,
the transient bound can be analyzed with the LMI below.
The Data
, and
The LMI:
The Euclidean norm of the state satisfies:
if there exists some 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 Discrete-Time 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.