The files in this directory implement the routines related to the self-triggered and optimal sampling. The user of this code may find more details of the theory behind these methods in the following papers

E. Bini, G. M. Buttazzo, Optimal Sampling Patterns for Linear Control
Systems, submitted to IEEE Transactions on Automatic Control.

In the explanation of these routines, we assume familiarity with these
papers.

All routines have been implemented as scripts and not as functions.
Hence, each script requires some "INPUTS" and produce some "OUTPUTS".
Inputs and outputs of the scripts are specified in the head of the
file. The code does not pretend to be particularly efficient. The goal
is only on showing the results, which are explained in the above
mentioned paper.

Below we list the files:

init1D.m
	Initializes a first-order system

init2D.m
	Initializes a special second-order system

tKfromTauK.m
	It simply computes the sampling instants from the sampling
	intervals

computeDiscDyn.m
	Computes the matrices describing the discrete-time dynamics,
	for a given sampling pattern.

computeDiscWeights.m
	Compute the discrete-time weighting matrices for a given
	sampling pattern

computeDiscRiccati.m
	Computes the Riccati matrices for a given sampling pattern

computeDiscRiccatiDiff.m
	Computes the derivative of the Riccati matrices w.r.t. to the
	sampling intervals

computeOptUk.m
	Compute the optimal control input and the corresponding state
	evolution.

optPeriodic.m
	Compute the cost for the periodic sampling.

optDensM.m
	Computes the sampling pattern according to a given power
	(provided as input) of the derivative of the optimal control
	input

optQuanta.m
	Compute the sampling sequence that minimizes the quantization
	error w.r.t. the optimal continuous-time input. This method is
	called "qua" in the paper. The method iterates the necessary
	condition for optimality.

computeAvgs.m
	Used by optQuanta to compute the average of the optimal
	control input over the sampling intervals

optNumeric.m
	Compute numerically the sampling sequence that minimizes the
	LQR control cost.  This method is called "num" in the paper
	and it is based on a simple gradient descent algorithm

plotCalpha.m
	Used to plot the asymptotic normalized cost for the methods
	that sample according to powers of the derivative of the
	optimal continuous-time input

plotCmWithN.m
	Used to plot the asymptotic normalized costs for several
	methods, as the number of sampling instants N varies