This is a state-of-the-art treatise on the problems of both nonlinearity and uncertainty in the dynamics and control of engineering systems. The concept of dynamics and control implies the combination of dynamic analysis and control synthesis. It is essential to gain insight into the dynamics of a nonlinear system with uncertainty if any new control strategy is designed to utilize nonlinearity.

Recent years have witnessed a rapid development of active control of various mechanical systems. With increasingly strict requirements for control speed and system performance, the unavoidable time delays in both controllers and actuators have become a serious problem. For instance, all digital controllers, analogue anti aliasing and reconstruction filters exhibit a certain time delay during operation, and the hydraulic actuators and human being interaction usually show even more significant time delays. These time delays, albeit very short in most cases, often deteriorate the control performance or even cause the instability of the system, be cause the actuators may feed energy at the moment when the system does not need it. Thus, the effect of time delays on the system performance has drawn much at tention in the design of robots, active vehicle suspensions, active tendons for tall buildings, as well as the controlled vibro-impact systems. On the other hand, the properly designed delay control may improve the performance of dynamic sys tems. For instance, the delayed state feedback has found its applications to the design of dynamic absorbers, the linearization of nonlinear systems, the control of chaotic oscillators, etc. Most controlled mechanical systems with time delays can be modeled as the dynamic systems described by a set of ordinary differential equations with time delays."

The concept of dynamics and control implies the combination of dynamic analysis and control synthesis. It is essential to gain insight into the dynamics of a nonlinear system with uncertainty if any new control strategy is designed to utilize nonlinearity. However, the new control strategy to be proposed must be robust enough so that any unexpected small disturbances will not alter the desired target of control. Such a concept is calling more attention to the modelling and simplification of dynamic systems subject to uncertain environment, the fine analysis and robust design of controlled dynamic systems resulting in new control strategies due to understanding of nonlinear phenomena and artificial intelligence, the combination of passive control, active control and semi-active control, as well as the interaction among sensors, controllers and actuators.

The time delays in controllers and actuators can either deteriorate or improve the dynamic performance of a controlled mechanical system. Thus, it is desirable to gain an insight into the effect of time delays on the dynamics of a practical system in its design phase. This monograph represents the recent advances in system modeling, analysis of stability, robust stability and bifurcation by using some new mathematical tools such as generalized Sturm criterion and Dixon's resultant elimination of polynomials. The theoretical results are demonstrated through a number of examples of active vehicle chassis, structure control, as well as the control of chaos of mechanical systems.