Analysis Of Systems Under State Saturation

Saturation nonlinearities are ubiquitous in engineering systems. In controlsystems, every physical controller, actuator or sensor is subject to saturation owing toits maximum and minimum limits. The saturation nonlinearities can be introduced intwo ways. The first one is for safety, such as the safety voltage, the highest or lowestlimit of liquid level, etc. The second one is inherent of the instruments, for example,the digital filters or neural nets systems with limit words. In spite of the origin of thesaturation, it is of great importance to analyze and design the systems with saturationnonlinearity because it will greatly influent the stability and performance of thesystems. Roughly speaking, there are two strategies for dealing with state saturation.One way is to neglect the saturation in the first stage, and then to add someproblem-specific schemes to deal with the adverse effects caused by saturation. Theseschemes may lead to improved performance but poorly understood stability properties.The other one is more systematic. It takes into account the saturation nonlinearities atthe outset of the design of the system. Or, in the case that a control law is designed apriori to meet either the performance or stability requirement. Consequently, thesecond one is used more widely, and is just the approach that we will take in thisdissertation. Several methods are proposed to analyze the stability of state saturationsystems and to design the state feedback for the former unstable systems.The stability and stabilization problem for state saturation linear systems isstudied in this dissertation. For state-space models, the problem of stabilization forcontinuous linear time-delay systems is studied on the basis of Lyapunov theory,convex theory and linear matrix inequality (LMI). The content of this dissertation canbe divided into two parts. The first one is to find new, less conservative theorems ofstability for systems under state saturation. The other one is to introduce theconclusions obtained in these systems to some ubiquitous but never been studied areasand find the criterions of stability for them, the state saturation systems withtime-delay, for example. The detailed content of this dissertation are outlined asfollows,1. The stability of continuous-time systems with state saturation is investigated.The sufficient and necessary condition for global asymptotic stability is obtained withanalysis. The effectiveness of the method is showed by comparing these conditionswith that planar systems have already presented.2. The stability of continuous-time systems with state saturation is investigated.New and less conservative conclusions are gained by improving the existed results. Iterative linear matrix inequality algorithms are proposed in order to use theseconclusions with the LMI toolboxes. The effectiveness of the method is demonstratedby numerical examples.3. The stability of discrete-time systems with state saturation is investigated.New theorems are obtained by using the existed method of continuous systems, that is,putting the saturation constrained states in a convexity.4. The stability of time-delay systems with state saturation is investigated. Thesufficient conditions are obtained by using the existed conclusions of state saturationand time-delay systems respectively. The conclusions can be used as a guide to designthe controller. Iterative linear matrix inequality algorithms are also proposed in orderto use these conclusions with the LMI toolboxes. The effectiveness of the method isshowed by several numerical examples.