The stability of non-conservative systems and an estimate of the domain of attraction

The exponential stability and stabilization of non-autonomous mechanical systems with non-conservative forces

“…For this case, Corollary 1 ensures exponential stability subject to the condition bk > supp(t). In this example, it is also impossible to use Agafonov's theorem 11 since the matrix of the gyroscopic forces in the system is a null matrix.…”

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

“…1-8 However, when non-conservative positional forces are present in the system, the total energy will no longer possess the properties of a Lyapunov function, making the problem of its construction more difficult to solve, although in a number of cases it is possible to obtain effective stability conditions along these lines. [9][10][11] In the case of extremely non-linear positional forces, the difficulties encountered in constructing the Lyapunov functions increase considerably.…”

“…1-8 However, when non-conservative positional forces are present in the system, the total energy will no longer possess the properties of a Lyapunov function, making the problem of its construction more difficult to solve, although in a number of cases it is possible to obtain effective stability conditions along these lines. [9][10][11] In the case of extremely non-linear positional forces, the difficulties encountered in constructing the Lyapunov functions increase considerably.A possible method of investigating stability in cases of this kind is the decomposition method, which consists of dividing the complex system into several simpler subsystems, studying them individually, and the valid transfer of the results obtained to the initial system. This method is being widely and effectively used in stability and control theory.…”

The stability of non-conservative systems with singular matrices of dissipative forces

“…Another approach to a stability analysis of non-conservative systems has been considered, using Lyapunov's direct method without the above-mentioned structural transformation of the initial system; but then, too, the matrix of dissipative forces was also assumed to be non-singular [5].…”