Improved design technique for uncertain multiple-input-multiple-output feedback systems†

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Abstract
This paper presents a synthesis technique for linear time invariant n×n multiple-input-multiple-output (MIMO) feedback systems with constrained ‘ plant’ P, and output feedback. Due to uncertainty, P is known only to be a member of a set &𝒫 = {P}. It is required for all Pεp, the n2 system transfer functions tuv be members of specified sets of acceptable outputs a uv;; u. v+ 1, [tdot] n. The problem is rigorously converted into a number of single-input-single output (SISO) uncertainty problems, whose solutions are guaranteed to solve the original MIMO problem. The technique has several advantages over previous ones : (1) fixed point theory is not needed to rigorously justify the theory—the justification is very simple ; (2) there is significantly less overdesign inherent in the method ; and (3) if arbitrary small sensitivity is desired over arbitrary large bandwidth, then the set p must satisfy certain constraints as 8→∞. It is shown that these constraints are inherent in all linear time invariant compensation techniques. In the old techniques, these con straints were always present, even in non-arbitrarily small sensitivity specifications.