Abstract
A technique is presented for studying the stability of equilibrium of linear lumped-parameter systems involving general types of forces such as dissipative, non-conservative, gyroscopic, and circulatory. A modified approach to solving the Liapunov equation is used to provide a function V which is exploited to present different stability criteria for the equilibrium of such systems. It was shown that this approach is advantagous to the solution of the Liapunov equation, since it is more computationally attractive. Additionally, this may be used to determine the effects of different parameters on the systems stability or to design a controller for an actively controlled system. Several previously developed related works are studied and compared with this work. Furthermore, examples are used to illustrate the presented approach and some of its applications.
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