An order-reduction approach for singular linear quadratic problem

A systematical transformation procedure for determining non-negativity and optimal control of a singular quadratic cost functional is introduced as an alternative to the existing transformation approaches. An order-reduction algorithm for singular linear quadratic problems is derived using the Riccati-like linear matrix inequality. The algorithm recursively yields a test of a set of simple algebraic conditions, and unifies the singular, partially singular, and non-singular problems.<>