https://www.researchgate.net/publication/316454836_LULC_analysis_of_urban_spaces_using_Markov_chain_predictive_model_at_Ranchi_in_India

https://www.researchgate.net/publication/306085974_Analysis_of_Urban_Sprawl_Dynamics_Using_Geospatial_Technology_in_Ranchi_City_Jharkhand_India

Article LULC analysis of urban spaces using Markov chain predictive ...

Article Analysis of Urban Sprawl Dynamics Using Geospatial Technolog...

As ESA provides open access to its image archives since spring 2017, you can use SAR data: Urban areas show considerably higher backscatter intensities than their surroundings.

ERS-1/2, ENVISAT, ALOS PALSAR, and Sentinel-1 can be used to create long time series. SNAP, for example, provides a module implementing the speckle divergence principle:

T. Esch, M. Thiel, A. Schenk, A. Roth, A. Müller, and S. Dech, "Delineation of Urban Footprints From TerraSAR-X Data by Analyzing Speckle Characteristics and Intensity Information," IEEE Transactions on Geoscience and Remote Sensing, vol. 48, no. 2, pp. 905-916, 2010.

T. Esch and A. Roth, “Semi-automated classification of urban areas by means of high resolution radar data,” in Proc. ISPRS Congr., 2004, pp. 478–482. 

M. Stasolla and P. Gamba, “Spatial indexes for the extraction of formal and informal human settlements from high-resolution SAR images,” IEEE J. Sel. Topics Appl. Earth Obs. Remote Sens., vol. 1, no. 2, pp. 98–106, Jun. 2008.

Software: http://step.esa.int/main/toolboxes/snap/

Tutorial: https://fromgistors.blogspot.com/2017/04/mapping-urban-area-with-sentinel-1-data.html

Data sources:

https://earth.esa.int/web/guest/eoli (ERS, ENVISAT)

https://scihub.copernicus.eu/dhus/#/home (Sentinel-1)

https://alos-palsar-ds.eo.esa.int/oads/access/ (ALOS PALSAR)

https://vertex.daac.asf.alaska.edu (JERS-1, Seasat, and also ALOS and Sentinel-1)

We studied the urban growth of Lima (Peru), see in

http://revistainvi.uchile.cl/index.php/INVI/article/view/875

My colleague studied urban growth in Cairo, but it is another study using remote sensing data: https://www.researchgate.net/publication/268400528_CHANGE_IN_THE_URBAN_SPATIAL_STRUCTURE_OF_THE_GREATER_CAIRO_METROPOLITAN_AREA_EGYPT

Another idea would be to check if there is maps from the past (official maps, e.g. for road-planning or for water supply) and then make the change visible over time with a succession of maps..

Article Change in the urban spatial structure of the Greater Cairo M...

The links provided by previous repondents all appear to be based on remote sensing technique.  It will be very interesting to see what other tools are available for this topic.  I guess census data might be useful.  In urban economics, density gradient is often estimated (e.g. Mills) to see if it flattens over time.  That's one way to measure urban growth, or more accurately, suburbanization, over time.  Similar, land price gradient or employment gradient can also be estimated for this purpose.  Any other tools?