New algorithm for H2 guaranteed cost control of singularly perturbed uncertain systems and its application to the manufacturing assembly process

The H₂ guaranteed cost control problem for a singularly perturbed norm-bounded uncertain system is addressed by using an improved recursive algorithm. First we derive sufficient conditions such that a full-order algebraic Riccati equation has a positive definite solution. After defining the generalized algebraic Riccati equation, we propose a new recursive algorithm based on the Kleinman algorithm with a very special kind of initial condition. The proposed algorithm is very efficient from the numerical point of view since the new recursive algorithm has the property of quadratic convergence. Furthermore, we apply the new algorithm to a manufacturing assembly process and show the validity of the proposed full-order controller