The burrobush is in the sunflower family and is of the same genus as ragweed and cheesebush.  Ambrosia dumosa is a small gray-green shrub that produces bur-like fruit and is sometimes called bur sage.  Many people are allergic to its pollen. 
This small shrub is often associated with creosote and white ratany.  In some areas of the Mojave desert, the 3 shrubs make up the majority of the perennial plants.