ltitr function

Time response of a Linear Time-Invariant system

ltitr Computes the time response of a Linear Time-Invariant system

ltitr(a, b, u, x0)

Arguments

• a: An n x n matrix of the state-space system
• b: An n x m matrix of the state-space system
• u: A row vector for single input systems. The input U must have as many rows as there are inputs in the system. Each column of U corresponds to a new time point. u could be generated using a signal generator like gensig
• x0: a vector of initial conditions with as many rows as the rows of a

Returns

Returns a matrix X which has as many rows as there are outputs y (and with max(dim(U)) columns).

Details

ltitr computes the time response of a Linear Time-Invariant system in state-space representation of the form: x[n+1] = Ax[n] + Bu[n] to an input, U

ltitr(a, b, u) computes the time response with zero-initial conditions since x0 is not supplied.

Examples

A <- diag(1, 2)
B <- rbind(1, 1)
x0 <- rbind(-1, -2)
u <- cbind(1, 2, 3, 4, 5)
X <- ltitr(A, B, u)
X <- ltitr(A, B, u, x0)

A <- replicate(6, abs(rnorm(6)))
B <- replicate(3, abs(rnorm(6)))
U <- replicate(100, rnorm(3))
x0 <-  rnorm(6)
X <- ltitr(A, B, U)
X <- ltitr(A, B, U, x0)

See Also

lsim gensig