Perturbation and error analysis considerations in robust control

• Main Author: Kawelke, Jens
• Published: University of Leicester 1997
• Subjects: 629.8
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.696287

This thesis deals with perturbation and error analysis in robust control, mainly H control, but the H2 norm is also considered. Perturbation analysis investigates the sensitivity of a solution or structure to perturbations or uncertainties in the input data. Error analysis is used to make statements about the numerical stability of an algorithm and uses results from perturbation analysis. Although perturbation and error analysis is a well-developed field in linear algebra, very little work has been done to introduce these concepts into the field of control. This thesis attempts to improve this situation. The main emphasis of the thesis is on H norm computations. Nonlinear and linear perturbation bounds are derived for the H norm. A rigorous error analysis is presented for two methods of computing the H norm: the Hamiltonian method and the SVD method. Numerical instability of the Hamiltonian method is shown with several examples. The SVD method, which is shown to be numerically stable, is updated with new upper and lower bounds for the frequency response between two given frequency points. Then using an upper frequency bound, a new algorithm is presented. This new algorithm can be implemented in a parallel process and has a similar performance to the Hamiltonian method in terms of computing time. In addition, nonlinear and linear perturbation bounds are derived for the H2 norm, and for the solutions of Lyapunov equations. Finally the H control problem is considered and perturbation bounds for the corresponding parameterized Riccati equations are derived. This leads to an estimation of the norm of the perturbation in the H controller.