Robust Analysis and Control of Stochastic Interval Systems

Abstract

Abstract. Stochastic interval systems is a new type of stochastic system in recent years, which is a new field integrated by information and control. This paper introduces the research history and the newest research trends of stochastic interval systems, and presents many widespread theoretical and application problems. Moreover, some new research topics and directions related to stochastic interval systems are proposed. IntroductionFor many problems in natural world, socio-economic, material systems of practical engineering, their dynamic rules can be described by deterministic dynamic model or random system model. The description of deterministic system model is by deterministic ordinary differential equations, which is to simplify the process of the actual system. Its system model is relatively simple, and is easy to analyze and synthesize, and its research tool is also relatively simple. When the considered system is under ideal conditions or system accuracy is not required, the system is often reduced to a deterministic model.Since the creation of modern control theory, control theory based on deterministic system model has been developing rapidly, and played an important role in practical applications. However, in many practical systems, such as engineering controls, traffic management, physical circuit system, the random factor is objective and inevitable. Due to the perturbations by the internal structure parameter, the system control inputs and the external environment, the established model can not accurately describe the controlled object or the system creates deviation between the running model and the actual object. In large-scale integrated circuits, interference of random factors is inevitable. To ignore the interference of random factors will increase the systematic errors and affect system performance. On the radio circuit receiving system, due to the random noise disturbance outside, the received signal of a radio is unstable. Thus, random factors are worth considering.With the development of science and technology, the system accuracy requirements of practical engineering technology become more and more high. The original simplified deterministic model can not meet the accuracy requirements of the system. The system designed by deterministic model in operation will deviate from predetermined design requirements, resulting in the generation of random deviation. Therefore, in the system modeling, we should fully consider the impact of random factors on the system, and use a stochastic model for system modeling and use the stochastic point of view for the system analysis and synthesis. Stochastic system model is described by stochastic ordinary differential equations. In a sense, the theory of stochastic systems are the combination product of deterministic systems theory and stochastic processes.In most actual operation of the control system, there are more or less uncertain factors, such as the measurement error of physical components, the impact of limited word length of memory, and outside in...