Robust Stability Analysis of Single-Parameter Dependent Descriptor Systems

Exact robust stability analysis is considered for time-invariant descriptor systems whose coefficient matrices are affine functions of an uncertain parameter. A necessary and sufficient condition for robust stability is given as a parameterized linear matrix inequality (LMI) whose variable matrices are polynomial matrices of the parameter, where an upper bound of the degree of the polynomial matrices with respect to the parameter is derived explicitly. Then, it is shown that the parameterized LMI is reduced to a parameter-independent and finite-dimensional LMI, which implies that robust stability analysis of this class of systems can be recast exactly as a finite-dimensional convex feasibility problem.