Abstract
Systems described by high order differential equations are discussed. Stability theory, especially Lyapunov theory is primarily a theory of systems described by first-order differential equations, by flows on manifolds. It is possible to develop a Lyapunov theory which makes it necessary to go through a state space representation. The theory of quadratic Lyapunov differential equations is based on two-variable polynomials. Two-variable polynomials, derivative polynomials, and Lyapunov functions are considered. Examples are included. >
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