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Necessary and Sufficient Conditions for Absolute Stability

Part of the Mathematical Modelling: Theory and Applications book series (MMTA, volume 25)

In this chapter, we discuss the necessary and sufficient conditions for absolute stability of various Lurie control systems described by ordinary differential equations. The absolute stability for all the system’s variables will be equivalently transformed into that of a single variable or partial variables, and that of the Hurwitz stability for matrix, which is easy to be verified. Based on obtained theoretical results, some practically useful algebraic sufficient conditions will be derived, which provide guidelines for designers and engineers. The material given in 4.1 and 4.3 is chosen from [78, 80] and that presented in 4.2 and 4.4 is based on [67, 76, 77]. The results given in 4.5 are mainly taken from [89].

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© Springer Science + Business Media B.V 2008

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