Parametric linear constant and gain-scheduled control systems design are studied for a class of linear parameter varying (LPV) systems and piecewise linear (PL) systems based on stabilization via convexity restrictions. Specifically, the maximum row sum (matrix) norm is utilized to obtain a computationally attractive state space method for the scheduling of simple linear controllers under incomplete modelling information. Furthermore, certain close connections of the studied framework with fuzzy gain scheduling are discussed.