Constrained global optimization of stringent inequalities (or equations) utilizing multivariate polynomials can be used to solve the challenges posed by robust stability analysis. For the purpose of constrained global optimization of multivariate functions, we offer techniques that are constructed using B-spline expansion. The branch-and-bound structure serves as the foundation for the proposed algorithms. By taking into account the robust stability analysis problem, we put the suggested fundamental restricted global optimization algorithms through their paces. The results obtained are consistent with those that have been published in the relevant literature