LMIs in Control/Click here to continue/Fundamentals of Matrix and LMIs/Nevanlinna Pick Interpolation with Scaling

Nevanlinna-Pick Interpolation with Scaling The Nevanlinna-Pick problem arises in multi-input, multi-output (MIMO) control theory, particularly robust and optimal controller synthesis with structured perturbations. The problem is to try and find such that is analytic in 1 em and define the scaling, and finally, 2 2 em 7 em The System The scaling factor is given as a set of block-diagonal matrices with specified block structure. The matrix valued function H({\lambda}) analytic on the open upper half plane is a Nevanlinna function if . The Nevanlinna LMI matrix is defined as . The matrix is a diagonal matrix of the given sequence of data points The Data Given: 2 Initial sequence of data points in the complex plane with . 2 Two sequences of row vectors containing distinct target points with , and with . The LMI: Nevanlinna- Pick Interpolation with Scaling First, implement a change of variables for and . From this substitution it can be concluded that is the smallest positive such that there exists a such that the following is true: 5 em , 5 em , 5 em Conclusion: If the LMI constraints are met, then there exists a norm-bounded optimal gain which satisfies the scaled Nevanlinna-Pick interpolation objective defined above in Problem (1). Implementation Implementation requires YALMIP and Mosek. - MATLAB code for Nevanlinna-Pick Interpolation. Related LMIs Nevalinna-Pick Interpolation 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 . Return to Main Page: LMIs in Control: https://en.wikibooks.org/wiki/LMIs_in_Control