A NUMERICAL-METHOD FOR CONSTRUCTING LYAPUNOV FUNCTIONS AND COMPUTER-AIDED ANALYSIS OF STABILITY OF NONLINEAR DYNAMIC-SYSTEMS

The problem of constructing Lyapunov functions, which involves the ana lysis of the stability of the equilibrium state of nonlinear time-inva riant systems, is considered. The problem of deriving a Lyapunov funct ion in the region which includes a deleted neighborhood of zero is red uced to a problem of linear programming. An algorithm is developed to verify the validity of the properties of the Lyapunov function realize d in the region of interest with the aid of the net-point method. The suggested numerical method used to construct Lyapunov functions enable s us to obtain the conditions of asymptotic stability, exponental stab ility, absolute stability, and also stability of the systems described by differential inclusions. All the results thus obtained can be exte nded to cover the discrete systems described by difference equations.