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By means of polynomial decomposition,a con- trol scheme for polynomial nonlinear systems with affine time- varying uncertain parameters is presented.The idea of poly- nomial decomposition is to convert the coefficients of polyno- mial into a matrix with free variables,so that the nonnegativity of polynomials with even orders can be checked by linear ma- trix inequality(LMI)solvers or bilinear matrix inequality(BMI) solvers.Control synthesis for polynomial nonlinear system is based on Lyapunov stability theorem in this paper.Construct- ing Lyapunov function and finding feedback controller are au- tomatically finished by computer programming with algorithms given in this paper.For multidimension systems with relatively high-order controller,the controller constructed with full mono- mial base will be in numerous terms.To overcome this problem, the reduced-form controller with minimum monomial terms is derived by the proposed algorithm.Then a suboptimal control aiming at minimum cost performance with gain constraints is advanced.The control scheme achieves effective performance as illustrated by numerical examples.
By means of polynomial decomposition, a con- trol scheme for polynomial nonlinear systems with affine time-varying uncertain parameters is presented. The idea of poly- nomial decomposition is to convert the coefficients of polyno- mial into a matrix with free variables, so that the nonnegativity of polynomials with even orders can be checked by linear matrit inequality (LMI) solvers or bilinear matrix inequality (BMI) solvers. Control synthesis for polynomial nonlinear systems is based on Lyapunov stability theorem in this paper. Construct Lyapunov function and finding feedback controller are au- tomatically finished by computer programming with algorithms given in this paper. For multidimension systems with relatively high-order controller, the controller constructed with full mono- mial base will be in numerous terms. To overcome this problem, the reduced-form controller with minimum monomial terms is derived by the proposed algorithm. Chen a suboptimal control aiming at minimum cost perf ormance with gain constraints is advanced. The control scheme achieves effective performance as illustrated by numerical examples.