Asymptotic stability of large scale dynamical systems using computer generated Lyapunov functions

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1983
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Nam, Boo
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Electrical and Computer Engineering

The Department of Electrical and Computer Engineering (ECpE) contains two focuses. The focus on Electrical Engineering teaches students in the fields of control systems, electromagnetics and non-destructive evaluation, microelectronics, electric power & energy systems, and the like. The Computer Engineering focus teaches in the fields of software systems, embedded systems, networking, information security, computer architecture, etc.

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The Department of Electrical Engineering was formed in 1909 from the division of the Department of Physics and Electrical Engineering. In 1985 its name changed to Department of Electrical Engineering and Computer Engineering. In 1995 it became the Department of Electrical and Computer Engineering.

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1909-present

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  • Department of Electrical Engineering (1909-1985)
  • Department of Electrical Engineering and Computer Engineering (1985-1995)

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The stability of equilibrium points of large scale dynamical systems described by differential equations of the form x = f(x) is analyzed using computer generated Lyapunov functions;Recently, Brayton and Tong developed a constructive algorithm for use in the stability analysis of dynamical systems; however, their method of analysis taxes the capabilities of most modern computers when applied to high dimensional systems. To circumvent these difficulties, we divide an interconnected system into lower order subsystems. Lyapunov functions of the isolated subsystems are constructed using Brayton and Tong's constructive algorithm. An aggregated text matrix for the stability analysis of the entire system is determined in terms of the qualitative properties of the isolated subsystems and in terms of the interconnecting structures of the entire system. If this matrix is an M-matrix, then the system is guaranteed to be asymptotically stable in some region;The above results are applied to a multimachine power system to estimate the stability region of the overall system, and to estimate the critical clearing time if the power system is faulted during its steady state operation. The results are also applied in stabilizing a long train control system so that the system is globally asymptotically stable.

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Sat Jan 01 00:00:00 UTC 1983