Documentation Center

  • Trial Software
  • Product Updates


Linear-quadratic (LQ) state-feedback regulator for discrete-time state-space system


[K,S,e] = dlqr(A,B,Q,R,N)


[K,S,e] = dlqr(A,B,Q,R,N) calculates the optimal gain matrix K such that the state-feedback law

minimizes the quadratic cost function

for the discrete-time state-space mode

The default value N=0 is assumed when N is omitted.

In addition to the state-feedback gain K, dlqr returns the infinite horizon solution S of the associated discrete-time Riccati equation

and the closed-loop eigenvalues e = eig(A-B*K). Note that K is derived from S by


The problem data must satisfy:

  • The pair (A, B) is stabilizable.

  • R > 0 and Q − NR–1NT ≥ 0

  • (Q − NR–1NT, A − BR–1NT) has no unobservable mode on the unit circle.

See Also

| | | |

Was this topic helpful?