A geometric solution to the simultaneous bounded domain stabilization problem

This paper presents an algorithmic method for solving the two-plant simulta neous bounded domain stabilization problem for SISO LTI systems. This probl em has no closed form solution. The solution provides robust performance in the presence of sensor or actuator failure, or other major parameter chang es. Vidyasagar (1987) studied a similar problem involving partially bounded stability domains. However, stability with respect to partially bounded do mains only partially bound performance characteristics, such as control ene rgy and transient response. The current investigation gives necessary condi tions for simultaneous bounded domain stability and demonstrates a geometry -based solution algorithm which can be automated. The possible solutions to the problem and the admissible solutions are represented as sets of points in Euclidean space. The solution to the problem is found by using computat ional geometric techniques to detect points in the intersection of these tw o sets, if there is one, and deducing the simultaneous stabilizing compensa tor design from the points found in the intersection.