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Design discrete linear-quadratic (LQ) regulator for continuous plant

`lqrd [Kd,S,e] = lqrd(A,B,Q,R,Ts) [Kd,S,e] = lqrd(A,B,Q,R,N,Ts) `

`lqrd ` designs a discrete
full-state-feedback regulator that has response characteristics similar
to a continuous state-feedback regulator designed using `lqr`.
This command is useful to design a gain matrix for digital implementation
after a satisfactory continuous state-feedback gain has been designed.

`[Kd,S,e] = lqrd(A,B,Q,R,Ts) `
calculates the discrete state-feedback law

that minimizes a discrete cost function equivalent to the continuous cost function

The matrices `A` and `B` specify
the continuous plant dynamics

and `Ts` specifies the sample time of the discrete
regulator. Also returned are the solution `S` of
the discrete Riccati equation for the discretized problem and the
discrete closed-loop eigenvalues` e = eig(Ad-Bd*Kd)`.

`[Kd,S,e] = lqrd(A,B,Q,R,N,Ts) `
solves the more general problem with a cross-coupling term in the
cost function.

[1] Franklin, G.F., J.D. Powell, and M.L.
Workman, *Digital Control of Dynamic Systems*,
Second Edition, Addison-Wesley, 1980, pp. 439-440.

[2] Van Loan, C.F., "Computing Integrals Involving
the Matrix Exponential," *IEEE ^{®} Trans. Automatic Control*,
AC-23, June 1978.

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