Study On Some Issues About Stability Analysis And Design For Switched Neutral Systems

A switched neutral delay system is an important category of hybrid systems. Due to interaction among the continuous dynamics and discrete dynamics and neutral time-delay is common in this kind of systems, many practical engineering issues can be described by switched neutral delay systems, the research of switched neutral delay systems is significant for both practice and theory. Based on Lyapunov stability theory, this dissertation mainly investigates the stability analysis and design of switched neutral delay systems by linear matrix inequalities method. The main contributions of this dissertation are as follows.Firstly, based on the relationship between time-delay and switching interval, the asymptotic stability of switched neutral delay systems under arbitrary switching sequence is discussed. The equivalent transformation is done to research the effect of configuration of subsystems to the stability of the whole system by Lyapunov functional method. Then sufficient conditions are given to guarantee asymptotic stability of switched neutral delay systems in term of linear matrix inequalities. Also, the design of state feedback controllers with memory is established.Secondly, exponential stability of switched neutral delay systems with fixed switching law is addressed. Since it is ture that state-dependent switching signals are usual in many switched control systems in real world, E-exponential stability of equivalent systems with fixed switching region is investigated by Lyapunov functional methods and inequalities analysis technique. Owning to the stability equivalence between the two systems, exponential stability of original system is obtained. Corresponding design of state feedback controllers are also accomplished on this basis.Thirdly, switching law design of a class of switched neutral delay systems is studied. If there is a Hurwitz linear convex combination of coefficient matrices for a class of neutral delay subsystems, asymptoticly stable regions of each subsystem can be found by dividing the state space properly. Based on the divisions of state space, switching law can be obtained by setting switching regions. Sufficient conditions of this kind of switched neutral systems are provided in term of linear matrix inequalities. Here, the stability of subsystems is not necessary, they are only required to satisfy certain conditions. Switching laws are crucial to stabilize the whole system in these problems. Switching state feedback controllers and switching laws can also be designed to make the close-loop system stable for those which do not meet the constraint conditions.Fouthly, the problem of robust non-fragile H_∞control is discussed for a class of uncertain switched neutral delay systems. H_∞performance of definite switched neutral delay systems is discussed in advance, and the condition of interior stability and design of corresponding state feedback controllers without memory are presented. These results are extended to uncertain switched neutral delay systems, influence of gain disturbance of controllers is also considered. And then, controllers of robust non-fragile with H_∞performance are obtained.Next, reliable guaranteed cost control problem of switched neutral delay systems is concerned. Based on the fact that actuators are nonideal in real control systems, a more practical system is constructed by using continuous faults model. Reliable guaranteed cost controllers with constraint of quadratic cost function are obtained by the method of Lyapunov functional. Upper bound of the cost function can be derived by optimal methods.Finally, the problem of robust sliding control of switched neutral delay systems is studied. Combined the Lyapunov method with Finsler's lemma, sliding surfaces and corresponding controllers of each subsystems are designed, which meet reching conditions and sliding mode conditions for switched neutral delay systems with linear fractional uncertainty under arbitrary switching laws. Based on these results, the design of single sliding surface and switching laws are also presented to make systems stable.At the end of the dissertation, the results are summarized and further research problems are pointed out.