Exponential stability for singular networked control system with dynamical state feedback

This study deals with the model, exponential stability and controller design problems of singular networked control system (NCS). Two new control methods of dynamical state feedback control and dynamical state feedback proportional-integral (PI) control for the NCS with time-delay and data packet dropout are addressed. Using two new control methods, the singular NCS is modeled as an asynchronous dynamical system (ADS) constrained by event rates. Furthermore, based on the ADS theory, principle of Lyapunov stability and method of linear matrix inequality, the semi-negative definite matrix conditions of exponential stability, the dynamical state feedback controller and the dynamical state feedback PI controller design for the NCS are given. Finally, numerical examples illustrate the feasibility of the proposed control methods of dynamical state feedback control and dynamical state feedback PI control, semi-negative definite matrix conditions of exponential stability and the controller design.

1 INTRODUCTION

In networked control system (NCS), there exist transmission time-delay and data packet dropout caused by the network. They have a certain impact on the stability of NCS, which is an important feature that reflects the normal operation state of the system. The NCS papers [1]~[3] proposed the exponential stability definition and fundamental theorem of asynchronous dynamical system (ADS), and discussed the negative definite matrix conditions of exponential stability for NCS with data packet dropout. Papers [4]~[6] considered the exponential stability and the asymptotic stability of NCS with data packet dropout. Papers [7]~[9] focused on the global exponential stability of model-based NCS. Papers [3], [10]~[13] also considered the exponential stability and the asymptotic stability of multi-packet transmission NCS. Papers [14]~[16] discussed the asymptotic stability and the robust stability of singular NCS. All these literatures and other literatures of NCS dealt with the NCS with static state feedback, static output feedback or dynamical output feedback. None of them discussed the dynamical state feedback control and dynamical state feedback proportional-integral (PI) control. However, proportional-integral-derivative (PID) control is the most widely applied basic control method in industrial control. For the singular NCS with time-varying delay and data packet dropout, this paper presents two new control methods, which are dynamical state feedback control and dynamical state feedback PI control. Meanwhile, the model of the singular NCS with time-varying delay and data packet dropout is constructed. The exponential stability and controller design method for the singular NCS are investigated. Finally, numerical examples are given to show the feasibility of the results.