Indefinite LQ Problem for Singular Systems
Ma Shu · Acta Automatica Sinica · 2006
The indefinite LQ problem (i.e., the weighting matrix in the quadratic cost has some negative eigenvalues) for singular systems is discussed. First, it is pointed out that the problem is solvable, and the sufficient and necessary condition that the problem can be transformed into singular LQ problem for singular systems is given. Then, based on the equivalent singular LQ problem, the sufficient condition that the problem has a unique optimal control-trajectory pair is given. Finally, an example is given to show the validity of the proposed conclusion.