GRADGN achieved a stability maximum. The run time for this example was 12 s on an IBM 360/50 computer.
VI. DISCUSSIONThe stabbility improvement technique described has been found to be a useful practical tool. It is especially useful for high-order systems having a small number of outputs. Its major limitation is that it determines a local rather than global stability maximum.A technique with a similar aim has been derived by Koenigsberg [3J. F€is technique was based on the Reddy [5] expression ax tr {conjoint [D] [ a~/ a a l 1 _ -aa t r {conjoint ID]] (9 ) where t r { 1 deiines the trace operation and conjoint [Dl Li adjoint [ D -XI]. Equations (7) and (9) are equivalent, but (7) can be readily shown to be computationally more efficient. REFERENCES 14 I 151 A. Jameson, "Design of a singleinput system for specified roots using DD. 345348. June 1970. output feedback," I E E E Trans. Automat. Contr. (Short Papers). vol. AC-15, E-. J. Daviion "On pole assignment in linear systems with incom lete state feedback," I B E E Trans. Adomat. Contr. (Short Papers), vol. A8-15, PP. 348-351, June 1970. linear systems, Ph.D. dissertation, Reneselaer Polytechnic Inst., Troy, Qj 3 0 and S'(t -T ) , X'(t -7 ) are some constant diagonal matrices with positive elements. In this case t.he weighting filters are pure integrators. Accelerated adaptation algorithms are obtained if Pj # 0, Qj # 0. Proof: Defining a new state vector z = z --? / (
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