Direct feedback control for polynomial nonlinear systems

A considerable class of nonlinear systems can be described or approximated by polynomial functions with sufficiently high order, therefore can be described in tensor notation compactly. For the plants with polynomial functions in the state and input, a globally stable feedback control, using finite-time tensor product of an augmented state vector, is designed in this paper. Combining the input with the ordinary state to form the augmented state vector, the plants are dealt with as uniformly like linear systems. The concept of a quotient set is used to discard redundant information in the design. A genetic algorithm is employed to complete the design. The relative proofs and simulation are presented.