LMIs in Control/Click here to continue/LMIs in system and stability Theory/KYP Lemma with Feedthrough
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Definition[edit | edit source]
Consider a square, continuous-time LTI system, , with minimal state-space realization (, , , ), where , , , and .
LMI 1.1[edit | edit source]
The system is positive real (PR) under either of the following equivalent necessary and sufficient conditions.
- There exists , where , such that .
- There exists , where , such that
This is a special case of the KYP Lemma for QSR dissipative systems with , , and .
LMIs 1.2[edit | edit source]
The system is strictly positive real (SPR) under either of the following equivalent necessary and sufficient conditions.
- There exists , where , such that .
- There exists , where , such that
This is a special case of the KYP Lemma for QSR dissipative systems with , , and , where .
External Links[edit | edit source]
- LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
- LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
- LMI Properties and Applications in Systems, Stability, and Control Theory - A downloadable book on LMIs by Ryan James Caverly and James Richard Forbes.