Stability Analysis Of Singular Networked Control Systems And Singular Time-delay Systems

Time-delays are often encountered in various dynamic systems and generally regarded as a main source of instability and poor performance in such systems. Over the past decades, much attention has been paid to these systems and many conclusions have been given in literature. However, many problems for time-delay systems are still needed to be considered.In terms of linear matrix inequality (LMI) technique and Lyapunov stability theory, two types of time-delay systems are considered:singular networked control systems and singular time-delay systems.The main work of this dissertation is as follows:1. The stability problem of continuous networked control systems is considered. Using frequency domain method and considering the characteristic root of the system characteristic equation, the stability problem of low-dimension networked control systems in high-speed is analyzed. Then, in terms of Lyapunov-Razumikhin functional method, the problem of robust stability for a class of generally continuous non-linear networked control systems is considered, some sufficient stabilization conditions are established.2. Using Lyapunov-Krasovskii functional method, state feedback controller for a class of multiple-input and multiple-output (MIMO) networked control systems is designed. The design method does not need any model transformation and bounding technique for cross terms, which can be obtained by solving a set of linear matrix inequalities.3. The mathematic models of singular networked control systems with the different driven modes of sensors, controllers and actuators, short time delay or long time delay, impulse or impulsive-free are developed. Based on the obtained models, we analyze the causality, controllability and observability of a type of singular networked control system with short time delay and the sensor nodes clock-driven, the controller and actuator nodes event-driven. The necessary and sufficient conditions of the causality, controllability and observability for singular networked control systems are presented.Based on the models of singular networked control systems, the stabilization problem is considered for a class of singular networked control systems (NCS) with networked-induced delay and data packet dropout. Firstly, the singular NCS can be modeled as an asynchronous dynamical system. Then, the sufficient condition of the exponential stability criterion is given. Moreover, the state feedback control law can be obtained by solving LMIs.The guaranteed cost control problem of singular networked control systems is analyzed. Using Lyapunov function and LMI technique, the state feedback controller is given, which can make the resultant closed-loop systems stable and satisfy the corresponding guaranteed cost.By the models of singular networked control systems with the sensors and the actuators time-driven, the controllers event-driven, and short-time delay, the problem of robust H∞control is discussed. At the same time, the whole system can be transferred into a discrete-time system. Then, the corresponding stability criteria and H∞state feedback controllers are constructed.4. The problem of delay-dependent robust stabilization for singular systems with multiple time-varying state delays has been investigated. Firstly, without any model transformation and bounding technique for cross terms, a delay-dependent stability criterion is established to ensure singular system regular, impulse free and stable. Based on the criterion, the problem is solved via state feedback controller, which guarantees the resultant closed-loop system regular, impulse free and stable for all admissible uncertainties.