Riccati conditioning and sensitivity for a MinMax controlled cable-mass system

— In this paper we study the relationship between the parameter θ, used in the design of the MinMax controller, and the conditioning of the approximate algebraic Riccati equations, the sensitivity of the eigenvalues of I −θ2PΠ to θ as well as the effect of θ on the stability radia and the stability margin of the system. In order to guarantee accurate numerical solutions to the approximate Riccati equations, the Riccati equations must remain well-conditioned for the values of θ that are considered. This condition number reflects the combined sensitivity of the Riccati equations to the system inputs A, B, R, C and θ. In addition, we also consider the sensitivity of the eigenvalues of I −θ2PΠ to θ. We study the possibility of these sensitivities serving as an indication of the largest value of θ for which I − θ2PΠ remains positive definite. This sensitivity could also serve as an indication of the accuracy of the computation of I −θ2PΠ. Lastly, in order to desig...

• Type: Conference
• Year: 2008
• Where: CDC
• Authors: Lizette Zietsman, Katie A. Evans, J. Teye Brown, Richard A. Idowu
• Keywords: Approximate Riccati Equations, CDC 2008, Control Systems, Riccati Equations, Stability Margins