Stability analysis of robust control problems in linear descriptor systems with matching conditions

Abstract

We investigate the optimal control equivalent and state feedback approach to linear time-invariant descriptor systems with norm-bounded uncertainty in matrix A(q). The goal is to find a controller that can stabilize the system even in the presence of random perturbations and to study the effect of initial conditions on the system’s stability. The systems with matching conditions and also linear algebraic equations with the full rank of the algebraic coefficient matrix are investigated.  The solution to the optimal control problem (OCP) for the linear descriptor system (LDS) is the solution to the robust linear descriptor control problem provided. We will show that with theorems and examples.