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Incremental output feedback design approach for discrete-time parameter-varying systems with amplitude and rate control constraints

In this work, we investigate an incremental stabilizing Output Feedback control law for discrete-time linear parameter-varying (LPV) systems subject to state constraints, control amplitude limits, and bounds of the control-rate variation. To this end, we consider the Positive-Invariance and Contractivity properties of polyhedral sets to guarantee the regional closed-loop stability and that the constraints are all respected. As usual in LPV literature, the varying parameters are considered online available. Furthermore, we describe the constrained control system in the extended state space composed of the system's state and control variables, in which the control variations act as the control inputs. From this extended LPV formulation, we use the known necessary and sufficient algebraic conditions for positive-invariance and contractivity to propose a new bilinear optimization problem to design the controller. The proposed objective function optimizes the polyhedron size in given directions, and an efficient non-linear optimization solver is used to tackle the present bilinearities. Numerical examples showcase the effectiveness and potential of our proposal.