Consistency of H∞ index and output variance constraints for descriptor systems

By satisfactory control theory, a design approach of state feedback controllers was proposed for a class of uncertain descriptor systems, such that the closed-loop descriptor system satisfied the consistency of constraint indices of admissibility, H infinity and output-variance. First, a necessary and sufficient condition was presented for the closed-loop descriptor system with admissibility and given H infinity constraints. Then via quasi-Newton approach, the solvability of nonlinear matrix inequality was transformed into the minimization problem of maximum eigenvalue. Controller design method was provided for state feedback control with constraints of admissibility, H infinity and consistency output-variance, and a range was presented for output-variance which was consistent with the given H infinity. Finally a numerical example is given to illustrate the results obtained and the design scheme provided.