The goal of this research is the development of new design methodologies for stabilizing uncertain systems. This will be achieved by effectively exploiting a priori knowledge of the structure of the uncertainties. Such information is often available in the detailed description of mechanical systems; e.g., aircraft. The research objectives include exploiting structure in three major areas: (1) In the design of observers. (ii) In designing state feedback controls via a special Riccati equation. (iii) In the stability analysis of families of (characteristic) polynomials. Lyapunov theory will be the major technical tool. Indeed, existing robustness criteria use Lyapunov theory either directly or indirectly. In the stability analysis of polynomials the celebrated results of Kharitonov will be invoked. It is expected that this research will help to establish a unified approach to stabilizing uncertain systems. The approach will avoid conservative robust designs (a trait of those existing methods which ignore available structural information) and synthesize stabilizing feedback controls. In contrast, many modern approaches take the control as given data and provide a robustness estimate for the closed loop system.
