Uniting two local output controllers for linear system subject to input saturation: LMI Approach

In this paper, we solve the problem of hybrid output unification of two local output feedback controllerU0 and U1 for linear systems subject to input saturation. The closed-loop system with the controller U0 has a smaller region of attraction R0 and higher decay rate σ0, while the closed-loop system with U1 has a larger region of attraction R1 and a slower decay rate σ1, R0⊂R1 and σ0 > σ1. To the best of our knowledge, the problem of unification of two local output feedback controller, has been solved only in the recent papers [17] and [2]. In [17], the problem of unification of two output controller is solved by using two norm estimators and a trigger time τ* to switch from the “global” controller to the “local” one, where it is defined in [17] and chosen sufficiently large. The work [2] proves that it can be selected arbitrarily small. Such choice of τ* minimizes the use of the slow controller U1 and, thus, ameliorates the performance significantly. In this paper, the solution of the unification problem is formulated by means of linear matrix inequalities (LMIs), which can be easily verified numerically. The numerical example given in this paper compares the performance of the proposed hybrid controller with hybrid controllers in [17] and [2].