A. Shapiro, "Duality, optimality conditions, and perturbation analysis," in Handbook of Semidefinite Programming: Theory, Algorithms, and Applications, H. Wolkowicz, R. Saigal, and L. Vandenberghe, Eds. Boston, USA: Kluwer, 2000, pp. 68--92. Home/Search Document Details and Download
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Investigating Duality on Stability Conditions - de Oliveira (Correct)
....for a rigorous proof. Comparing Lemmas 1 and 3, we notice that besides the qualitative time domain versus frequency domain duality, the given tests are also mathematical duals. In fact, by defining the Lagrangian function L(P, Q) trace Q AQ QA it follows from duality theory [4] that which shows that the stability conditions in Lemmas 1 and 3 are indeed duals. This fact is the main motivation of this paper. In the next sections we depart from the recently developed (time domain) Lyapunov stability analysis tool given in [1] aiming at the derivation ....
....program (14) is given by s.t. 0. # # # # # # # # # # # # # # # . 18) Before using these problems to characterize stability it is necessary to verify to what extent the solution of the duals indeed provide useful information. It follows from duality theory (see, for instance, [4]) that # i , i = 2 . A straightforward conclusion is that 0, i = and, therefore, that the system (1) is not asymptotically stable whenever # i or # i , i = 2 are positive. The complementary statement, that is, # i 0, # i 0, i = which would enable us to conclude on ....
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A. Shapiro, "Duality, optimality conditions, and perturbation analysis," in Handbook of Semidefinite Programming: theory, algorithms and applications (H. Wolkowicz, R. Saigal, and L. Vandenberghe, eds.), pp. 68--92, Boston, MA: Kluwer Academic Press, 2000.
Probabilistic design of a robust controller using a.. - Oishi (2004) (Correct)
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A. Shapiro, "Duality, optimality conditions, and perturbation analysis," in Handbook of Semidefinite Programming: Theory, Algorithms, and Applications, H. Wolkowicz, R. Saigal, and L. Vandenberghe, Eds. Boston, USA: Kluwer, 2000, pp. 68--92.
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