On Stability of a Class of Linear Systems with Distributed and Lumped Parameters

• Published in: Mechanics of solids Vol. 54; no. 2; pp. 245 - 250
• Main Authors: Bairamov, B. F., Bairamov, F. D.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.03.2019; Springer Nature B.V
• Subjects: Classical Mechanics; Elasticity; Evolutionary computation; Liapunov functions; Linear systems; Mathematical analysis; Ordinary differential equations; Parameters; Partial differential equations; Physics; Physics and Astronomy; Quadratic forms; Stability; quadratic forms; systems with distributed and lumped parameters; method of Lyapunov functions; stability
• ISSN: 0025-6544; 1934-7936
• DOI: 10.3103/S002565441903004X

The method of Lyapunov functions is used to investigate the stability of systems with distributed and lumped parameters, described by linear partial and ordinary differential equations. The original high-order partial differential equations are represented by a first-order system of partial differential evolution equations and constraint equations; to do that, we introduce additional variables. Passing to the first-order system of partial differential equations and representing ordinary differential equations in the normal Cauchy form, we obtain a possibility to construct the Lyapunov function as a sum of integral and classical quadratic forms and develop general methods of the investigation of the stability of a broad class of systems with distributed and lumped parameters. For example, we consider the stability of the work of the wind-driven lift pump and take into account the elasticity of the shaft transmitting the torque from the wind engine to the pump.