Lyapunov function computation for autonomous systems with complex dynamic behavior

A computational approach is presented in this paper to construct local Lyapunov functions for autonomous dynamical systems with multiple isolated locally asymptotically stable (such as point-like, periodic, or strange) attractors. We consider of nonlinear ODEs, where the right-hand-side dynamic equations given form rational (i.e., fraction polynomials). The function searched a parameterized quadratic terms state variables. decomposition state-dependent inequalities performed using linear fractional transformation (LFT) and further algebraic/numeric simplification steps. Unlike sum squares (SOS) approach, sufficient matrix inequality (LMI) conditions are formulated only on compact polytopic subset space, which allows indefinite solutions decomposition. solution enforced affine annihilators Lagrange multipliers. Alongside typical conditions, boundary LMI constraints prescribed Finsler’s lemma ensure required geometric properties function. results illustrated four planar benchmark models having either equlibria limit cycle, Lorenz system.