A hybrid polytopic partition approach to constrained stabilization of bilinear systems

Stabilization of a class of bilinear systems is investigated in this paper, i.e., bilinear systems which are affine in the input. Such systems often appear in a variety of fields, e.g., power electronics or system biology. A novel approach to synthesis of piecewise affine (PWA) control laws for this class of systems is proposed. It exploits the concept of hybrid polytopic partition (HPP) which efficiently combines the partition of the control law with the conic partition induced by the polyhedral control Lyapunov function. The approach is beneficial on three separate levels. It provides guarantees of asymptotic stability to the closed-loop system in presence of hard constraints on system states and inputs. The synthesis method is computationally advantageous as it relies on solving separate linear programs for each affine control gain. The third advantage comes from the fact that the synthesis method exploits predefined polytopic partition of the control law, which can be tailored a priori to the available hardware resources. The approach is further extended to accommodate a one-step-ahead prediction optimization of the system response with respect to a specific criteria.