Passive observer-based controller design for a class of Lipschitz nonlinear time-varying systems with application to Hepatitis B disease

Abstract

In this paper, a novel passive formulation has been developed based on LMI to design passive state-observer for a wide range of Lipschitz nonlinear systems. During this formulation, a stable and strictly passive state-observer is provided in order to have passive closed-loop system. A new interconnection between passivity of subsystems and passivity/stability of the total closed-loop system has been presented. In this regard, some theorems are defined based on virtually Euler-Lagrange form of passivation. Due to using this form and the proposed theorems, the design process will simplify and speed up. A passivity-based control based on passive state-observer has been proposed to control the hepatitis B virus infection disease. The reliability of the proposed controller/observer has been examined using MATLAB/SIMULINK, where the simulation results and the sensitivity analysis demonstrate the capability of this novel approach.