mpt_dlqr

MPT_DLQR Linear-quadratic regulator design for discrete-time systems.

 ---------------------------------------------------------------------------
 DESCRIPTION
 ---------------------------------------------------------------------------
 Calculates the optimal gain matrix K such that the state-feedback law
 u = -K*x minimizes the cost function

           J = Sum {x'Qx + u'Ru}

 ---------------------------------------------------------------------------
 INPUT
 ---------------------------------------------------------------------------
 A, B     - Matrices defining the dynamics; x^+=A*x+B*u
 Q, R     - Weighting matrices

 ---------------------------------------------------------------------------
 OUTPUT                                                                                                    
 ---------------------------------------------------------------------------
 K        - Optimal state-feedback
 P        - Common quadratic Lyapunov function V(x)=x'Px for feedback law K
 E        - E = EIG(A - B*K)