The stability and stabilization of non-linear, non-stationary mechanical systems

On input‐to‐state stability Lyapunov functions for mechanical systems

“…This assumption formulates the same properties as Assumption 1, considering nonlinear potential forces and linear dissipative ones (in Assumption 1 the potential forces are linear). Then the system equation can be rewritten as follows: and using the approach proposed in Reference 14, let us select a LF in the form: where $$$ h>0 $$$ is a design parameter, then Hence, (6) is GSLF for a sufficiently big value of $$$ h $$$ for the system (2) under Assumption 2. Let us demonstrate that a mild modification is needed to get ISS:…”