Some Topics On The Control Theory Of Finite Time Stability

Finite time stability is a new concept, which is quite different from the classical stability. It is recently attracting considerable interests. According to the actual background, many complex problems can be described as finite time stable problem. The recent decades have witnessed the great development of researches on the study of finite time stability, which plays a significant role in designing the satellite orbit and chemical engineering. In this paper, with the help of linear matrix inequality and using Lyapunov functions, we discuss the finite time stable problem on different systems. To be concrete, the contributions of this dissertation are as follows:In recent years, multi-agent systems have received more and more attention due to the potential applications of multi-agent systems in many different areas including cooperative control of vehicle formations, cooperative control of unmanned air vehi-cles (UAVs), congestion control in communication networks, swarm-based computing, design of distributed sensor networks and so on. In multi-agent systems, agents may ex-perience abrupt changes of states at certain time instants. These maybe due to changes in their neighbors, sudden environment changes, etc. To describe mathematically an evolution of a real process with a short-term perturbation, it is sometimes convenient to consider these perturbations in the form of impulses. In biological systems, some states may correspond to unfavorable of dangerous situations. Furthermore, we de-scribe the uncertainties in the systems as robust. In chapter two, we first introduce definition of finite time stable. Then we study the finite time stability of multi-agent systems with impulsive effects and robust, and some sufficient conditions are obtained for the finite time stability. We proved that for impulsive systems, the communication graph could be unconnected, which is less conservative than results in some papers.In chapter three, we investigate the finite time stable of nonlinear impulsive sys-tem. By using a new concept called average impulse interval (All), less conservative conditions are obtained for the FTS problem on the impulsive systems. Then we consider the linear time-invariant sampled-data systems by modeling such systems as linear impulsive systems. It is proved that when the All of a sequence of impulsive signals ζ is equal to Υα, the upper bound of the impulsive intervals could be very large, while the lower bound of the impulsive intervals could be also small enough.In chapter six, we consider the the finite time stability and L2-gain analysis for switched positive linear systems.sufficient conditions in terms of linear matrix in-equalities (LMIs) for the finite time stability of switched positive linear systems are obtained. Furthermore, under asynchronous switching, L2-gain analysis is developed for switched positive linear systems with average dwell time (ADT).