LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/Non-Expansivity and boundedness Realness

This section studies the non-expansivity and bounded-realness of a system. The System Given a state-space representation of a linear system are the state, output and input vectors respectively. The Data are system matrices. Definition The linear system with the same number of input and output variables is called non-expansive if : 1 hold for any arbitrary , arbitrary input , and the corresponding solution of the system with . In addition, the transfer function matrix : 2 of system is called is positive real if it is square and satisfies : 3 LMI Condition Let the linear system be controllable. Then, the system is bounded-real if an only if there exists such that : 4 and : 5 Implementation This implementation requires Yalmip and Mosek. https://github.com/ShenoyVaradaraya/LMI--master/blob/main/bounded_realness.m Conclusion: Thus, it is seen that passivity and positive-realness describe the same property of a linear system, one gives the time-domain feature and the other provides frequency-domain feature of this property. 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. LMIs in Control Systems: Analysis, Design and Applications - by Guang-Ren Duan and Hai-Hua Yu, CRC Press, Taylor & Francis Group, 2013 Return to Main Page: