Research On Analysis Of Complex Switched System And Its Applications In Networked Systems

Switched system is an important class of hybrid systems, which has wide physical backgrounds and practical applications. The research on switched system is related to many control problems, such as robot control and vibration isolation control. Therefore, analysis and synthesis of the switched system are of significant scientific and practical values. Due to the interaction of continuous dynamics and discrete switched signals, the switched sys-tem has very complex dynamics. It brings many interesting yet challenging research topics to control community and other related fields. On the other hand, nonlinear disturbance, stochastic fluctuation and time delays appearing in practical systems also interacts with the switching signals, which add much more difficulties to analysis and syntheses of such a class of complex switched systems. This dissertation is concerned with the analysis and synthesis of a class of switched systems with nonlinear disturbance, stochastic fluctuation, time delays and parameter switchings. Moreover, the approaches proposed for the complex switched system will be applied to solve the analysis and synthesis problems for networked fault detection and filtering systems. The main work is summarized as follows:1. The H∞filtering is investigated for a class of nonlinear stochastic switched systems with random measurement delays. Due to interactions of the stochastic noise, feedback delay, nonlinearity and switching mechanism, analysis of such complex systems is chal-lenging. Based on the stochastic system analysis method and the Lyapunov stability theory, a sufficient condition is obtained such that the filtering error system is exponentially stable in the mean-square sense and achieves a prescribed H∞performance level. The corre-sponding filter design method is also presented by restricting the parameterized matrices. The effectiveness of the main results is illustrated by a numerical simulation of genetic reg- ulatory networks.2. The asynchronous H∞filtering is discussed for a class of nonlinear switched sys-tems with both state delay and switching delay. By constructing a piece-wise Lyapunov functional and using the average dwell time analysis method, a sufficient condition is de-rived such that the filtering error system is exponentially stable and achieves a prescribed H∞performance level. The relation between the asynchronous time and the system per-formance is explicitly established. The effectiveness of the proposed design algorithm is finally illustrated by a simulation study of neural networks.3. The H∞filtering problem is investigated for of a class nonlinear stochastic switched system with missing measurements. A further consideration of nonlinear disturbance, stochastic disturbance and mixed time delays extends existing results. Specifically, a new compensation strategy is proposed for the measurement missing problem. By using the av-erage dwell time analysis method and the Lyapunov stability theory, a sufficient condition is derived such that filtering error system is exponentially stable in the mean-square sense and achieves a prescribed H∞performance level. Based on this condition, a design method for the optimal filter.4. For a class of discrete-time singular switched system with static limitation and state delay, the H∞filtering problem is firstly investigated by using the average dwell time switching method. By introducing a novel lemma and constructing an appropriate Lya-punov functional, a sufficient condition is derived such that the filtering error system is regular, causal and exponentially stable. Based on this condition, a filter design method is also presented. The effectiveness of the proposed design method is illustrated by a numeri-cal simulation of an input-output system in economic systems.5. Modeling and analysis for networked fault detection of fuzzy systems in the frame-work of the concerned complex switched system are investigated. The networked fault detection of fuzzy systems with medium access constraints and random packet dropouts is firstly studied. By modeling the fault detection system as a fuzzy time delay switched system with a stochastic variable, a sufficient condition is derived based on the complex switched systems analysis method such that the fault detection system is exponentially sta-ble in the mean-square sense and achieves a prescribed H∞performance level. Then, the networked fault detection problem with limited time slots is considered, and a simultaneous consideration of sensor saturation, signal quantization and packet dropouts approximate the real networked fault detection systems more closely. By modeling the fault detection sys-tem as an uncertain fuzzy switched system with multiple stochastic variables, a sufficient condition is derived such that the fault detection system is exponentially stable in the mean-square sense and achieves a prescribed H∞performance level. The main results are verified via some numerical examples.6. The H∞filtering of the wireless sensor networks in the proposed complex switched system framework is discussed. Due to the limited energy resource in the wireless sensor networks, a novel signal transmission strategy consisting of time-varying transmission in-tervals is proposed to reduce the energy consumption of sensors, and the centralized H∞filtering and distributed H∞filtering problems are investigated respectively. By modeling the filtering error system as a switched system with multiple stochastic variables, sufficient conditions are derived based on complex switched systems analysis method such that the filtering error systems are exponentially stable in the mean-square sense and achieve a pre-scribed H∞performance level. The relation between the signal transmission process and system performance is established. The effectiveness of the filter design is illustrated via the simulation studies of the spring-mass system.