Linear-Quadratic Regulator (LQR) design
[K,S,e] = lqr(SYS,Q,R,N)
[K,S,e] = LQR(A,B,Q,R,N)
For a continuous time system, the state-feedback law u = –Kx minimizes the quadratic cost function
subject to the system dynamics
In addition to the state-feedback gain K, lqr returns the solution S of the associated Riccati equation
and the closed-loop eigenvalues e = eig(A-B*K). K is derived from S using
For a discrete-time state-space model, u[n] = –Kx[n] minimizes
subject to x[n + 1] = Ax[n] + Bu[n].
[K,S,e] = LQR(A,B,Q,R,N) is an equivalent syntax for continuous-time models with dynamics
In all cases, when you omit the matrix N, N is set to 0.
The problem data must satisfy:
The pair (A,B) is stabilizable.
R > 0 and .
has no unobservable mode on the imaginary axis (or unit circle in discrete time).