LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/Tangential Nevanlinna Pick

Tangential Nevanlinna-Pick The Tangential Nevanlinna-Pick arises in multi-input, multi-output (MIMO) control theory, particularly robust and optimal control. The problem is to try and find a function which is analytic in and satisfies 5 3 em 5 em with 15 em The System is a set of matrix valued Nevanlinna functions. The matrix valued function H({\lambda}) analytic on the open upper half plane is a Nevanlinna function if . The Data Given: 2 Initial sequence of data points on real axis with ,2 And two sequences of row vectors containing distinct target points with , and with . The LMI: Tangential Nevanlinna- Pick Problem (1) has a solution if and only if the following is true: Nevanlinna-Pick Approach 5 em 2 Lyapunov Approach N can also be found using the Lyapunov equation: 5 em where The tangential Nevanlinna-Pick problem is then solved by confirming that . Conclusion: If is positive (semi)-definite, then there exists a norm-bounded analytic function, which satisfies 3 em 5 em with Implementation Implementation requires YALMIP and a linear solver such as sedumi. - MATLAB code for Tangential Nevanlinna-Pick Problem. Related LMIs Nevalinna-Pick Interpolation with Scaling 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. Generalized Interpolation in by Donald Sarason. Tangential Nevanlinna-Pick Interpolation Problem With Boundary Nodes in the Nevanlinna Class And The Related Moment Problem by Yong Jian Hu and Xiu Ping Zhang. <noinclude> Return to Main Page: LMIs in Control: https://en.wikibooks.org/wiki/LMIs_in_Control