The quadratic stability of a discrete-time system with structured uncertainties is studied by extending the concept of quadratic stability. When the system has no objective constraint, designing a controller is realized by solving LMIs and closed-loop quadratic stability is guaranteed. When the system has objective constraints, we design a controller by solving a dynamic programme problem with LMI constraints and also realizing a closed-loop quadratic stability. Moreover, LMIs for I/O saturation, state constraint and convergence rate constraints have been presented. Results and conditions all described by standard LMI problems construct a unified and systematic synthesis of plant with structured uncertainty.