Output Stabilization of Linear Systems in Given Set

Abstract

This paper presents a method for designing control laws to achieve output stabilization of linear systems within specified sets, even in the presence of unknown bounded disturbances. The approach consists of two stages. In the first stage, a coordinate transformation is utilized to convert the original system with output constraints into a new system without constraints. In the second stage, a controller is designed to ensure the boundedness of the controlled variable of the transformed system obtained in the first stage. Two distinct control strategies are presented in the second stage, depending on the measurability of the state vector. If the state vector is measurable, a controller is designed using state feedback based on the Lyapunov method and Linear Matrix Inequalities (LMIs). Alternatively, if only the output vector is measurable, an observer-based controller is designed using a Luenberger observer. In this case, the state estimation error does not need to converge to zero but must remain bounded. The efficacy of the proposed method and the validity of the theoretical results are demonstrated through simulations performed in MATLAB/Simulink.

Keywords

• linear dynamical system
• change of coordinates
• stability
• control
• linear matrix inequalities