A convex problem formulation to solve the linear quadratic problem for singular systems

We propose a new formulation of the infinite-horizon linear-quadratic regulator problem (ILRP) for descriptor systems. For this, we show that a solution to the ILRP can be found by solving a relatively simple convex parametric optimization problem. This gives an alternative to the relative tedious computation of the solution of the generalized Riccati equation in the case of descriptor systems