Primal-dual interior methods for biaffine matrix inequality problems in control

An efficient primal-dual interior method for solving biaffine matrix inequality problems is proposed. Some extensions of Newton's method is also proposed for nonconvex optimization problems. The proposed methods can be applied to synthesizing robust controllers, static output feedback controllers, mixed H/sub 2//H/sub /spl infin// controllers, mixed H/sub 2//H/sub /spl infin// PID controllers, etc. Which can be obtained by solving biaffine or linear matrix inequality problems. An explicit algorithm is also provided using the matrices in control problems.