## Contents

## LTIITR

Calculates an LTI state-trajectory

## Syntax

`x = ltiitr(A,B,u,w,x0)`

## Description

In its most general setting, this function iterates the state equation of an linear time-inavriant (LTI) system. It computes the state *x(k)* for *k* = *1,2,...,N* satisfying the LTI state equation:

This function is used internally by `dfunlti`, `dac2b`, `dac2bd`, `dinit` and `dltisim`. It is not meant for stand-alone use.

## Inputs

`A` is an LTI state-transition matrix of size *n* x *n*

`B` is an LTI input matrix of size *n* x *m*.

`u` is a *N* x *m* matrix containing *N* samples of the *m* inputs.

`w` is a (optional) *N* x *n* matrix containing the process noise.

`x0` is the (optional) initial state, an *n* x *1* vector.

## Outputs

`x` is the computed state, an *N* x *n* matrix.

## Algorithm

A direct iteration of the system's state-transition equation is used to obtain the state-trajectory for all time-instants.

## Used By

`dfunlti`, `dac2b`, `dac2bd`, `dinit`, `dltisim`