Kalman–Yakubovich–Popov lemma

The Kalman–Yakubovich–Popov lemma is a result in system analysis and control theory which states: Given a number γ > 0 {displaystyle gamma >0} , two n-vectors B, C and an n x n Hurwitz matrix A, if the pair ( A , B ) {displaystyle (A,B)} is completely controllable, then a symmetric matrix P and a vector Q satisfying The Kalman–Yakubovich–Popov lemma is a result in system analysis and control theory which states: Given a number γ > 0 {displaystyle gamma >0} , two n-vectors B, C and an n x n Hurwitz matrix A, if the pair ( A , B ) {displaystyle (A,B)} is completely controllable, then a symmetric matrix P and a vector Q satisfying