Considering a discrete-time linear parameter- varying (LPV) systems with input constraints, the paper deals with the co-design of a parameter-dependent state- feedback controller and a new parameter-dependent event- triggering mechanism. Two independent event-triggering policies are introduced at the sensor node to economize the limited network resources. They indicate whether the current state or the current scheduling parameters should be transmitted to the controller or not. In this sense, the controller scheduling parameters can differ from those of the system, yielding a certain degree of robustness con- cerning parameter deviations. Sufficient conditions, given in terms of linear matrix inequalities (LMIs), ensure the re- gional asymptotic stability of the closed loop. To formulated them, we use the Lyapunov theory along with the gener- alized sector condition. Moreover, we formulate a convex optimization procedure indirectly reducing the transmis- sion activity over the network. The proposed methodology effectiveness is attested through numerical examples and comparisons with related works from the literature.