ROBUST H1 CONTROLLER FOR BILINEAR SYSTEMS BY LINEAR MATRIX INEQUALITIES - (NIM: 30111001), SOLIKHATUN
Bilinear systems are a simple class of nonlinear systems which are linear in the states and inputs but not linear in both. Bilinear systems can be obtained naturally from the real problems or by doing the Carleman bilinearization of nonlinear system. In general, the obtained bilinear system is a high order system, so it will be difficult to analyze, simulate and control design of the related system. Therefore, it is important to reduce the order of a bilinear system and to design the reduced order controller. Bilinear system where the order is lower than the order of the original bilinear system is called the reduced bilinear system. Next, the original bilinear system is called a full order bilinear system. Criteria for selection of the order of the reduced bilinear system is introduced based on the value change of the least upper bound for the difference bilinear system in the proposed S2-norm. The difference bilinear system is performed by the transfer function difference between the full order bilinear system and the reduced bilinear system. The reduced bilinear system is similar to the full order bilinear system by using these criteria. The design of robust H1 controller that involve the uncertainty of model, internal and external disturbances implies the order of closed loop system is greater than or equal to the order of plants. Therefore, the reduced order controller for bilinear systems is needed for the implementation. The important information can be lost by model order reduction or controller reduction. Therefore, it is directly designed the reduced order controller. It is a generalization of the reduced order controller design of linear system for the bilinear systems. The robust H1 controller is a controller for the closed loop system that involve the H1 optimization. By using the H1 optimization, the closed loop system is being perfectly robust for the uncertainty of the model, internal and external disturbances. The existence of robust H1 full order and minimum order controller for bilinear systems are presented in this dissertation. A robust H1 controller can stabilize the closed loop system and it has a good performance. The full order robust H1 controller for bilinear systems is designed by using two approaches that are fuzzy and non fuzzy approaches. The fuzzy approach is done by presenting the bilinear system as a convex combination of many linear systems by using the Takagi-Sugeno fuzzy concept. The existence and formulation of the full order robust H1 controller for bilinear systems are presented in the linear matrix inequalities (LMIs). The non fuzzy approach is done by using the standard method, which the full order robust H1 control problem for bilinear systems is formulated by using the Riccaty equation. The solvability conditions of the robust H1 control problem for bilinear systems are formulated in LMIs. Because the LMIs set is a convex set, then the full order robust H1 control design problem is a convex optimization problem. The minimum order robust H1 controller is a robust H1 controller, which the lowest order. It can stabilize the closed loop system and produce a good performance, which be tolerated in optimal bounds. The solvability conditions of the reduced order robust H1 control problem for bilinear systems are presented in LMIs by rank constraint. Because the LMIs by rank constraint is a non-convex set, then the reduced order robust H1 control design problem is a non-convex optimization problem. Next, the performance of the minimum order robust H1 controller for bilinear systems is discussed.