Output feedback design for discrete-time constrained systems subject to persistent disturbances via bilinear programming
Stephanie L. Brião, Eugênio B. Castelan, Eduardo Camponogara, Jackson G. Ernesto
Abstract
In this work, we use the Δ-Invariance property of polyhedral sets to design a stabilizing Static Output Feedback (SOF) for linear discrete-time systems subject to persistent disturbances, assuring the states and control constraints fulfillment. We deduce new algebraic conditions to guarantee that any trajectory emanating from the Δ-Invariant polyhedron remains in it and converges in finite-time to another polyhedral set around the origin, where the trajectory remains ultimately bounded. Thus, the proposed SOF solution for the constrained control problem also requires determining the Δ-invariant and the ultimately bounded polyhedra. Therefore, the proposal considers a bilinear optimization problem whose objective function weighs the two associated polyhedral sets’ size and whose constraints are formed by the invariance relation. Moreover, an efficient non-linear optimization solver is used to tackle the present bilinearities. Numerical examples showcase the effectiveness and potential of our proposal.