LMIs in Control/KYP Lemmas/KYP lemma for continous time QSR dissipative system
The System
[edit | edit source]Consider a contiuous-time LTI system, , with minimal state-space realization (A, B, C, D), where and .
The Data
[edit | edit source]The matrices and
The Optimization Problem
[edit | edit source]The system is QSR disipative if
where is the input to is the output of and .
LMI : KYP Lemma for QSR Dissipative Systems
[edit | edit source]The system is also QSR dissipative if and only if there exists where such that
Conclusion:
[edit | edit source]If there exist a positive definite for the the selected Q,S and R matrices then the system is QSR dissipative.
Implementation
[edit | edit source]Code for implementation of this LMI using MATLAB. https://github.com/VJanand25/LMI
Related LMIs
[edit | edit source]Kalman%E2%80%93Yakubovich%E2%80%93Popov_lemma
References
[edit | edit source]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