Multiobjective Analysis And Synthesis Of Nonlinear Stochastic Systems

In this thesis,the multiobjective analysis and synthesis problems are discussed for several classes of stochastic nonlinear systems with time delays.In each chapter, the analysis problems are firstly considered that include the stability analysis, robust performance analysis and/or H_∞performance analysis problems,where the aim is to derive sufficient conditions such that the resulting systems are robustly asymptotically or exponentially stable in the mean square,for all possible nonlinear disturbances,external stochastic disturbances,Markovian switching,time delays as well as uncertain parameters.Then,the controller or filter synthesis problems are tackled where sufficient conditions are derived to ensure the existence of the desired controllers or filters.The existence conditions are characterized by the solution to a set of either linear matrix inequalities(LMIs) or Hamilton-Jacobi inequalities(HJI). The compendious frame and description of the thesis are given as follows:●In Chapter 1,the research background and motivation are discussed,the outline and contribution of the thesis are introduced,and the research problems to be addressed in each individual chapters are also highlighted.●In Chapter 2,we deal with the robust stability and stabilization problems for a class of stochastic time-delay interval uncertain systems with nonlinear dis-turbances by developing delay-dependent analysis techniques,where the It(?)'s differential formula,the Lyapunov stability theory and linear matrix inequality method are intensively used.●In Chapter 3,the robust stabilization and robust H_∞control problems for a class of stochastic time-delay uncertain systems with Markovian switching and nonlinear disturbance are investigated,where the nonlinear disturbance includes the time-delay term that is also mode dependent.●In Chapter 4,the H_∞filtering problem is addressed for a class of nonlinear time-delay It(?)-type stochastic systems,where the nonlinearities satisfy a special Lipschitz condition constraint.●In Chapters 5,the H_∞output feedback controller and filter design problems are dealt with for a class of stochastic time-delay systems with nonlinear disturbances, sensor nonlinearities and Markovian jumping parameters.A unified delay-dependent approach is developed to design the H_∞controller/filter for the stochastic delay jumping systems such that,for the addressed nonlinear disturbances and sensor nonlinearities,the dynamics of the augmented system is stochastically stable with a prescribed disturbance rejection attenuation levelγ.●In Chapter 6,the H_∞analysis problem is discussed for a general class of nonlin-ear stochastic systems with time-delays,which are described by general stochas-tic functional differential equations by using the Razumikhin-type method.●Chapter 7,in this chapter,the results of the above chapters are applied in the genetic regulatory networks,the information lost of sensors and networked control systems.Firstly,the filtering problem is concerned for a class of nonlinear genetic regulatory networks with state-dependent stochastic disturbances as well as state delays.The feedback regulation is described by a sector-like nonlinear function.The true concentrations of the mRNA and protein are estimated by designing a linear filter with guaranteed exponential stability of the filtering augmented systems.Then,the filtering problems is addressed for a class of discrete-time stochastic nonlinear time-delay systems with sensor information dropout and stochastic disturbances.The sensor measurement missing is assumed to be random and different for individual sensor,which is modeled by individual random variable satisfying a certain probabilistic distribution on the interval[01].Such a probabilistic distribution could be any commonly used discrete distributions.Finally,the filtering problem is addressed for a class of discrete-time stochastic nonlinear networked systems with multiple random communication delays and random packet losses.The communication delay and packet loss problems,which are frequently encountered in communication networks with limited digital capacity,are modeled by a stochastic mechanism that combines a certain set of indicator functions dependent on the same stochastic variable.●In Chapter 8,we summarize the results of the thesis and present the future works which may be further investigated.