Gradient systems have some particularly simple properties. They cannot exhibit oscillatory behaviour and their stability can be investigated using a natural Lyapunov function that can always be found by integration. An arbitrary dynamic system can be represented as the sum of a gradient system and a conservative system. An analysis of the system in its decomposed form is shown to lead to a Lyapunov-like algorithm. The algorithm can be applied to yield directly a graphical indication of the qualitative behaviour of nonlinear second-order systems.

Inspec keywords: nonlinear systems; gradient methods; Lyapunov methods; stability; nonlinear control systems

Other keywords: system decomposition; Lyapunov function; arbitrary dynamic system; nonlinear second order systems; gradient system; stability; conservative system

Subjects: General system theory; Interpolation and function approximation (numerical analysis); Nonlinear control systems