Optimal and robust control of a group of single-input linear systems using linear uncertain technique

Optimal and robust control of a group of single-input linear systems are presented. The formulation of the optimal state feedback controller is developed for a group of linear systems derived from a nonlinear system under attractive domains. Choosing a particular linear system as the desired model, the rest of the systems are assumed to be parameter-uncertain. Selection of a suitable weighting matrix for the performance index is used as a key method to optimally control this particular system and robustly stabilize the rest of the linear systems, simultaneously. It is shown that the above problem can be solved if an algebraic Riccati equation (ARE) has a solution. The state weighting matrix of this ARE can be linearly formulated for all uncertain coefficients and factors. If the weighting matrix is selected to satisfy certain constraints, the solution of ARE is positive, and all closed loop systems are stable. Control of a group of linearized longitudinal motions of an aircraft is employed to illustrate the potential of the proposed method.