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1.( AND U&SYN TH ESIS For example let△μ△6L-,△∈C×, Aa 0a.ca6.na Find amax△spp(A+BA(I-D△-)C). 1△.≤μ Define△△ 4. Then a bisection search can be done to find ama△ △.22 Related MATLAB Commands4 unwrapp.muunw rap.dypert.sisorat 10.3 Structured Robust Stability and Performance 10.3.1 Robust Stability The most well-known use of u as a robustness analy sis tool is in the frequency domain. Suppose G(s)is a stable,realrational,multiinput,mlti-output transfer function of a linear system For clarity,assume G has qu inputs and Pu outputs.Let be a block structure,as in equation(10.1),and assume that the dimensions are such that =/Cxp.We want to consider feedback perturbations to G which are themselves dy namical sy stems with the block-diagonal structure of the set = Let M(=)denote the set of all block diagonal and stable rational transfer functions that have block structures such as = M(=):△{△()eRH<:△(so)e=far all soCo} Theorem 09 Let 3>0.The loop shown below is well-posed and internally stahle oral△()∈M(=)with‖△ll≤<台if and only if su吧A(G(j3)≤3 ωR e_ +W- G() AND SYNTHESIS For example let I C A B C D Find max sup A BI DC Dene I Then a bisection search can be done to nd max M A B C D Related MATLAB Commands unwrapp muunwrap dypert sisorat Structured Robust Stability and Performance Robust Stability The most wellknown use of as a robustness analysis tool is in the frequency domain Suppose Gs is a stable realrational multiinput multioutput transfer function of a linear system For clarity assume G has q inputs and p outputs Let be a block structure as in equation and assume that the dimensions are such that C q p We want to consider feedback perturbations to G which are themselves dynamical systems with the blockdiagonal structure of the set Let M denote the set of all block diagonal and stable rational transfer functions that have block structures such as M RH so for all so C Theorem Let The loop shown below is wellposed and internally stable for all M with kk if and only if sup R Gj e e e e w w Gs