The variable gradient method for generating liapunov functions

Sufficient conditions for the stability of a class of second order systems

“…The VGM was first introduced in [8] and is a systematic tool for constructing Lyapunov functions. Consider the second-order nonlinear systeṁ…”

“…Second, it provides stronger stability results, in particular exponential and input-to-state stability, by deriving strict Lyapunov functions. These objectives are achieved by building suitable Lyapunov functions by means of the Variable Gradient Method (VGM) [8].…”

Stability analysis and synthesis of multivariable fuzzy systems using interval arithmetic

“…For example, Krasovskii's method allows to prove the su cient conditions for asymptotical stability of nonlinear systems. Other methods could be Schultz-Gibson's [35] one (the variable gradient method for generating Lyapunov functions), Lur'e's method [23] (some methods for constructing Lyapunov functions), etc.…”

Stability of Certain Nonlinear Differential Equations Using the Second Method of Liapunov

“…However, in most cases-sucha Liapunov function can rarely be obtained. The procedure presented in this section is seen to be similar to the "variable gradient method" [3] developed recently. In the conventional approach a V (x) > 0 is selected as a candidate for a Liapunov function and the conditions the parameters of the system have to satisfy to make 4 (x) <0 are determined to establish the stability conditions.…”