Stability Analysis And Controller Design For Uncertain Networked Control Systems

Networked control systems (NCS) are closed loop feedback systems constituted by real-time network. There are several advantages for NCS, which are given as follows, but not limited to less wire, less cost of installation, easy maintenance, higher flexibility and reliability, better fault detection ability, etc. However, some problems such as network-induced delay, packet dropout, multi-packet transmission and timing disorder are usually aroused due to band-limited channels, so the use of a network may deteriorate the performance or cause instability.Firstly, the state feedback stabilization problem for networked control system (NCS) with network-induce delay less than one sampling period is given. Establishing a new discrete-time linear system model of closed-loop NCS, the uncertainty caused by loop time-delay is converted to the matrix parameter uncertainty of the equation of the controlled plant, according to the Lyapunov theory and the linear matrix inequality (LMI), the asymptotic stability condition for the obtained closed-loop NCS is derived, which establishes the quantitative relation between the stability of the closed-loop NCS and two delay parameters, namely, the allowable delay upper bound and the allowable delay variation range. And a delay-dependent state feedback controller is designed. the controller can achieve the closed-loop network control system is asymptotically stable.Secondly, the guaranteed cost controller design for networked control system (NCS) with network-induce delay less than one sampling period is given. To solve the problem of uncertain time delay in networked control systems, the uncertainty of time delay is converted to the uncertainty of parameter matrixes, and the model of NCS is simplified as an uncertain discrete model with time delay. The guaranteed cost control problem for NCS is translated to a robust guaranteed cost control problem for an uncertain discrete system with time delay based on the above model. Lyapunov theory and linear matrix inequality (LMI) were applied to prove the sufficient condition of guaranteed cost control for NCS was equivalent to solving a LMI by a static state feedback. Simulation results show effectiveness of the proposed control method.Finally, the problem of robust H∞controller design for NCS via digital communication is addressed. The systems under consideration are stabilized via state feedback, where the network-induced delay and packet dropout are considered. The NCS is regarded as a time-delay system, and a new Lyapunov-Krasovskii functional, which is based on both the lower and upper bounds of time-varying network-induced delay. Robustly exponential stability and a prescribed H∞performance level for NCS with admissible uncertainties are discussed based on time-delay system theory, cone convex optimization theory and linear matrix inequality (LMI) approach. Maximum allowable delay bound of NCS is obtained by solving a convex optimization problem. At the same time, quantized feedback stability criterion of NCS with nonlinear perturbation is proposed such that the closed-loop NCS are robustly exponentially stable.