This paper introduces a new method to solve Liapunov stability problems for time invariant nonlinear systems—the normal determinative function method. The topic is split into six parts: review of the construction of...This paper introduces a new method to solve Liapunov stability problems for time invariant nonlinear systems—the normal determinative function method. The topic is split into six parts: review of the construction of a V(x) function, the modified Liapunov theorem form while the derivative of V(x) is definite, polynomial features of the analytic system’s normal determinative function V(x), judgment of definitiveness for a polynomial, coefficient direct solution method and the stabilty judgment of critical nonlinear systems, and future research.展开更多
文摘This paper introduces a new method to solve Liapunov stability problems for time invariant nonlinear systems—the normal determinative function method. The topic is split into six parts: review of the construction of a V(x) function, the modified Liapunov theorem form while the derivative of V(x) is definite, polynomial features of the analytic system’s normal determinative function V(x), judgment of definitiveness for a polynomial, coefficient direct solution method and the stabilty judgment of critical nonlinear systems, and future research.
