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In this article, we consider the output feedback eigenvalue assignment problem for

continuous and discrete–time control systems. This problem is formulated as unconstrained matrix optimization problems and tackled by the Nelder–Mead simplex

method and particle swarm optimization method. The two methods are extended to

compute the approximate solutions of the eigenvalue assignment problem for the particular cases of decentralized and periodic control systems. The performance of the

methods is demonstrated numerically on several test problems from the benchmark

collection [22] as well as other test examples from the system and control literature.

The bacterial strain (Bacillus subtilis) was isolated from soil sample using different composed culture for alkaline protease production in Submerged Fermentationby. The eight different submereged media were prepared to study of enzyme activity. Then the effect of pH, carbon sources nitrogen sources, Nacl concentration and metal ions on protease production were studied. The results indicated to: MD8 produced highest amount of alkaline protease (62.5 U /ml), The extracted crude enzyme was precipitated using varied precentages of ammonium sulphate was studied. The effect of pH,carbon,nitrogen sources sodium chloride concentration and metal ions was studied here and results tom maximum enzyme activity was as pH11 to MD4(17.97U/ml),glucose showed maximum yield in MD2(49.21U/ml) ammonium chloride affected maximum (132.81U/ml) to MD6 and the maximum activity was seen in case of MD5 with 11%NaCl(46.09U/ml) and lastly the metal ions effect was Mncl2(85.94U/ml))