This paper gives an elementary proofof Kharitonov's Theorem using simple complex plane geometry. Kharitonov's Theorem is a stability result for classes of polynomials defined by letting each coefficient vary independently in an arbitrary interval. The result states that the whole class is Hurwitzif andonly if four special, well-defined polynomials are Hurwitz.The paper also gives elementary proofs of two previously known extensions: for polynomi als of degree less than six, the requirement is reduced to fewer than four polynomials; and the theorem is generalized to polynomials with complex coefficients. Finally, we apply Kharitonov's Theorem and the generalized stability theorem to find sufficient (but conservative) conditions for a class of polynomials to be £7-Hurwitz for certain sets U of "undesirable" polynomial zero loca tions in the complex plane.
In this paper we derive several graphical U-Hurwitz tests for certain classes of linear time-invariant systems; we also derive finite tests based on these. The classes are defined in terms of their characteristic functions --polynomials for finite-dimensional systems, and the undesirable set U may be any closed subset of the complex plane. The analysis is motivated by our elementary proof of Kharitonov's Stability Theorem.
Systems are becoming increasingly interdependent and interconnected and the enterprise charged with developing such systems faces a challenge in ensuring that these dependencies are known and well understand such that the enterprise's portfolio of programs, projects and systems is balanced and robust. Enterprise Systems Engineering (ESE) is an emerging discipline that is designed to handle the challenges of helping to manage this portfolio and ensuring that the various mission and business systems are developed in a coherent, efficient and effective manner. This paper describes the desired features of an ESE capability that can help the enterprise manage its portfolio as well as addressing the various non‐system solutions that must be brought to bear. The strategy for realizing this ESE capability is described in terms of the goals and objectives that the enterprise should be expected to achieve.
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