Controller Design for Constrained Discrete-Time Uncertain Linear Systems Using Implicit Functions

This letter shows a controller design procedure for constrained discrete-time uncertain linear systems, where the control law and piece-wise functions implicitly defined by ramps give the associated invariant set and Lyapunov function. This structure enables non-symmetric invariant sets of larger sizes than other structures, yielding symmetric invariant sets. The procedure is iterative, and each iteration solves a semi-definite program. A simulation example illustrates the attributes of the proposed design procedure.