LMIs in Control/Stability Analysis/KYP Lemma With Feedthrough

Definition Consider a square, continuous-time LTI system, , with minimal state-space realization (, , , ), where , , , and . LMI 1.1 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 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 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.