Synthesis of systems with periodic solutions satisfying

A number of papers in the last decade dealt with synthesizing a set of coupled differential equations which have particular globally stable desired solutions, usually periodic. The methods for deriving these differential equations and verifying the properties of the solution have been, at best, ad hoc. This paper investigates the generic and stable synthesis of such systems which have the common property that the desired particular solutions satisfy constraint equations . The stability and generic properties are inherent and easily derived from basic properties of the function . First, Lyapunov techniques are used to guarantee that solutions satisfy the constraints. Next, well-known properties of manifolds are used to show that satisfying the constraint equations is a natural way to guarantee that solutions have particular useful properties. Further, these properties are generic in that almost all such possible have them. The synthesis properties are reapplied to the problems of the earlier papers. The resulting systems are more general and/or simpler to implement than those originally devised.