Control of Sector-Bound Systems with the Guarantee Output Signal in a Given Set

Abstract

In this paper, we propose a new method for synthesizing the control of plants with sector-bound nonlinearity with a guarantee of finding the controlled signal in given set at any time under conditions of unknown bounded disturbances. The basis of the method consists of two stages. At the first stage, the coordinate transformation is used to reduce the original constrained problem to the problem of studying the input-to-state stability of a new extended system without constraints. Thus, any known control methods can now be applied to stabilize the system in new coordinates. At the same time, to achieve the goal, it is not required to reduce the value of the control error. It is enough to show its boundedness. At the second stage, a control law is synthesized for the extended system, where the adjustable parameter is selected from the solution of linear matrix inequalities. To illustrate the effectiveness of the proposed method, simulation in the MATLAB Simulink is given. The simulation results show the presence of controlled signals in the given set and the boundness of all signals in the control system. It is shown that an increase the value of the gains in the control law improves the quality of disturbance attenuation that is consistent with theoretical results.