LMIs in Control/KYP Lemmas/KYP lemma for continous time QSR dissipative system

The System Consider a contiuous-time LTI system, , with minimal state-space realization (A, B, C, D), where and . The Data The matrices and The Optimization Problem The system is QSR disipative if where is the input to is the output of and . LMI : KYP Lemma for QSR Dissipative Systems The system is also QSR dissipative if and only if there exists where such that Conclusion: If there exist a positive definite for the selected Q,S and R matrices then the system is QSR dissipative. Implementation Code for implementation of this LMI using MATLAB. https://github.com/VJanand25/LMI Related LMIs Kalman%E2%80%93Yakubovich%E2%80%93Popov_lemma References 1. J. C. Willems, “Dissipative dynamical systems - part I: General theory,” Archive Rational Mechanics and Analysis, vol. 45, no. 5, pp. 321–351, 1972. 2. D. J. Hill and P. J. Moylan, “The stability of nonlinear dissipative systems,” IEEE Transac- tions on Automatic Control, vol. 21, no. 5, pp. 708–711, 1976. 3. LMI Properties and Applications in Systems, Stability, and Control Theory, by Ryan James Caverly1 and James Richard Forbes2