Static Output Feedback Control For Several Types Of Dynamic Systems

In recent years,as an important method in control theory and applications,static output feedback control has drawn an increasing attention.This is due to the fact that the state is not always accessible and only partial information through the measured output is available.On the other hand,static output feedback controllers are less expensive to implement and more reliable.Moreover,there are different kinds of complex dynamics in the actual systems,such as impulsive behavior,time delay,strong coupling,and so on.In this case,singular systems,rectangular systems,time-delay systems,fuzzy systems,switched systems,etc.,can better describe the actual processes with complex dynamics.Based on the current research findings for static output feedback of various of systems,this thesis will utilize Lyapunov stability theory,and various inequality techniques to study the stability and the static output feedback control methods for linear systems,singular systems,time-delay systems,rectangular systems,etc.,and develop new stability criteria,and static output feedback control design scheme.The main results of this thesis are as follows.1.Static output feedback control method for linear systems are studied.In order to solve the problem of non-convergence in the existing path-following method,we propose a new linearization method,and obtain an improved path following method which is proved to be convergent.To solve the problem of weak global search ability of improved path-following method,by the equivalent transformation on the conditions,we present the initial value optimization algorithm.Combining with the initial value optimization algorithm,the improved path-following method has a better search ability.In addition,a new stabilization condition is obtained by equivalent transformation of the structure of Lyapunov function which is also a BMI problem.However,only a small number of variables is fixed,the condition can be transformed into an LMI problem.A new method for solving the static output feedback control problems is constructed by combining the initial value optimization algorithm with the new stabilization condition.Different forms of continuous systems and discrete systems of the above methods are given.2.For continuous and discrete systems,the static output feedback control problem of singular systems are studied,respectively.Because the Lyapunov matrices of singular systems are no longer strictly positive definite,some algorithms for linear systems,such as the initial value optimization algorithm,can not be directly used.For continuous systems,we study a new path-following method for singular Markov jump systems with generally uncertain transition rates.By solving an LMI optimization problem,Step 1 of the algorithm is able to obtain good initial values,which avoids the application of the initial value optimization algorithm.For discrete systems,we study the singular fuzzy systems,and give a new sufficient condition for static output feedback control problems.Based on this condition,the modified cone-complementary linearization method is constructed.3.Stability analysis and static output feedback control problems for continuous and discrete time-delay systems are studied,respectively.For a class of continuous T-S fuzzy systems with time delay,a new stability criterion is obtained by constructing a new augmented Lyapunov-Krasovskii functional and applying a lower conservative Wirthingerbased integral inequality.For continuous singular time-delay systems,we study the mixed and passive control problems.By using the integral inequality in [83],new stability and stabilization criteria are obtained,and a new algorithm for solving the static output feedback controller is constructed.For discrete time-delay systems,we first give two new finite-sum inequalities.Then we obtain the new stability and stabilization conditions,which are less conservative.Static output feedback controller is solved by the initial value optimization algorithm and the improved path-following method.Finally,for the discrete singular T-S fuzzy systems with time delay,by using one of the new finite-sum inequality and the augmented Lyapunov-Krasovskii functional,we obtain new stability and stabilization conditions,and the modified cone-complementary linearization method is used to solve the static output feedback controller.4.The stabilization problem for rectangular fuzzy discrete-time systems with time delay is studied.A dynamic compensation is designed to ensure that the close-loop system is square,and a necessary and sufficient condition is proposed to guarantee the existence of a dynamic compensation with which the close-loop system is regular and causal.Moreover,the conditions in terms of bilinear matrix inequalities are derived to guarantee the admissibility of the closed-loop system.The modified cone-complementary linearization method is used to solve the conditions.