A Descriptor System Approach to Robust Stability Analysis and Controller Synthesis

This note revisits the problem of robust stability analysis and synthesis via parameter dependent Lyapunov functions. A descriptor system approach is taken to deriving linear matrix inequality conditions for robust stability and robust stabilizability of the polytopic systems and the affine parameter systems. Under these robust stabilizability conditions, state feedback laws that achieve robust stabilization are also constructed. The developed results can be viewed as a continuous-time counterpart of the discrete-time results by Oliveira et al. The effectiveness of the proposed analysis and synthesis approach is demonstrated by numerical examples.