With the wide use of computer networks and the continuous development of information processing and communication technologies, the study on integrating information theory and control theory has attracted considerable attention in recent years. The introduction of communication channels in control systems enhances their performance, but inevitably brings some challenging issues, such as network-induced time delay, data packet dropouts, quantization, and medium access constraint. With these undesirable effects, the performance of the network-based control systems can be adversely affected and the systems can even be destabilized in some cases. Therefore, it is of great significance to investigate how to avoid or alleviate the adverse effects of these communication constraints, and develop new approaches for analysis and synthesis on network-based control systems subject to these communication constraints. In this thesis, we consider the control/estimation problem of network-based systems with one or more communication constraints. Firstly, a kind of controller design method for a class of linear networked control systems (NCSs) with multiple packet dropouts is presented, where the numbers of consecutive packet dropouts in uplink and downlink channels are limited by known upper bounds. A novel model that can be used to describe multiple packet dropouts in both sensor-to-controller and controller-to-actuator sides is proposed. By constructing a new Lyapunov function and introducing some slack matrix variables, a sufficient condition for mean-square asymptotic stability is derived for the closed-loop networked control system, which is dependent on the upper bound of the number of packet dropouts. The corresponding state feedback control law is presented in terms of linear matrix inequalities (LMIs), which can be solved efficiently by using existing LMI optimization techniques. As it is known that two or more aspects of the aforementioned limited communication issues may simultaneously be encountered when dealing with the network-based systems, another controller design method for linear network-based systems with communication constraints on both uplink and downlink channels is developed, where the network-induced transmission time-delay, packet dropouts, and signal quantization are considered simultaneously. To deal with the phenomenon of quantization, a novel approach is adopted which converts the quantized state and control signal into a kind of actuator saturation with bounded external disturbances. Based on a proposed Lyapunov-Krasovskii functional, the existence conditions of a linear memoryless state feedback controller are derived, and an estimation method for the domain of admissible initial conditions is proposed from which all solutions for the systems concerned converge exponentially to an ellipsoid with a prescribed convergence rate. Besides the studies on linear systems, much research effort has been devoted to the problems of control and estimation for nonlinear network-based systems. We first investigate the problem of H∞ output feedback control for a class of nonlinear network-based systems subject to communication constraints, where the nonlinear systems are represented by T-S fuzzy models. The communication constraint concerned is that only one sensor node and one actuator node can access the shared network, which is the case in network environment. The accessability of the sensor nodes and/or actuator nodes is determined by medium access control with a prescribed probability. The attention is focused on the design of a piecewise static output feedback controller such that the closed-loop system is stochastically stable with a guaranteed H∞ performance. Based on a piecewise quadratic Lyapunov functions together with some matrix inequality convexifying techniques, an approach to the design of H∞ output feedback controller is proposed in terms of linear matrix inequalities. Finally, we study the problem of H∞ filtering for a class of nonlinear discrete-time systems with measurement quantization and packet dropouts. Each output is transmitted via an independent communication channel, and the phenomenon of packet dropouts in transmission is governed by an individual random binary distribution, while the quantization errors are treated as sector-bound uncertainties. Based on a piecewise-Lyapunov function, an approach to the design of H∞ piecewise filter is proposed such that the filtering error system is stochastically stable with a guaranteed H∞ performance. Some slack matrices are introduced to facilitate the filter design procedure by eliminating the coupling between the Lyapunov matrices and the system matrices. The filter parameters can be obtained by solving a set of linear matrix inequalities (LMIs). Furthermore, we extend the proposed filtering design to the problem of generalized H2 filtering. Simulation results are provided to show the effectiveness of the developed methods.