Computation of multiple type-one equilibrium points on the stability boundary using generalized fixed-point homotopy methods

This paper presents an efficient algorithm for the computation of all or multiple type-one equilibrium points (i.e., equilibrium point where the Jacobian has exactly one negative eigenvalue) for nonlinear systems. This algorithm is based on homotopy-continuation approaches and is devised to reduce the difficulty of choosing a set of proper initial points which converge to the set of all the type-one equilibrium points on the stability boundary (the boundary of the domain of attraction). The computational complexities for this algorithm and other existing algorithms including reflected gradient methods are discussed. The method is shown to be very efficient and reliable from numerical simulations