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LMIs in Control/Click here to continue/LMIs in system and stability Theory/Discrete-Time Transient
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Transient Impulse Response Bound
The System
For a single-input multi-output continuous-time LTI system with state-space realization
where , and .
The Data
, and .
Also it is assumed that Z(t)=CB be the unit impulsive response of the system.
The LMI:
If the Euclidean norm of the impulse response satisfies.
and if there exist and ,where P > 0, such that
Conclusion
This LMI can be used to analyze the Transient Impulse Response Bound for the given system
Implementation
This LMI can be used in a problem and can be solved using the solvers like Yalmip,sedumi,gurobi etc,.
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