A nonlinear minimization approach to multiobjective and structured controls for discrete‐time systems

In this paper, a nonlinear minimization approach is proposed for multiobjective and structured controls for discrete‐time systems. The problem of finding multiobjective and structured controls for discrete‐time systems is represented as a quadratic matrix inequality problem. It is shown that the problem is reduced to a nonlinear minimization problem that has a concave objective function and linear matrix inequality constraints. An algorithm for the nonlinear minimization problem is proposed, which is easily implemented with existing semidefinite programming algorithms. The validity of the proposed algorithm is illustrated by comparisons with existing methods. In addition, applications of this work are demonstrated via numerical examples.