Treatment Of Unconventional Observational Data And Robust Stabilization Of Uncertain Large-Scale Systems

This paper investigates the treatment of observational data in unconventional situations and robust stabilization of uncertain large-scale systems. The detection methods of outlying observations under several conventional distributions, the parameter estimation of several conventional distributions based on incomplete observation data and robust stabilization of uncertain large-scale systems with time-delay are mainly discussed.Nowadays, the detection of outlying observations and the parameter estimation of incomplete observation data have attracted great attention both in theoretical and application fields. In the first chapter, a brief introduction is given to describe the research background, recent situation and application instances of the unconventional observational data.In the second, the third and the fourth chapters, the detection methods of outlying observations are discussed based on various population distributions. Concerning several conventional distributional population, such as normal distribution, exponential distribution, extreme value distribution, and Weibull distribution, the popular detection methods of various of outlying observations are investigated. It is mainly discussed that if several outlying observations occur in sample observational data that affect the detection, a new method of outlying observations detection based on order statistic should be given to achieve preferable test statistic with better robustness. In the second chapter, concerning the specialty ofexponential distributions, taken the median which lies in the medial of the order statistics of a sample as reference, using the quotient of maximum to median of a sample and the quotient of minimum to median of a sample as unusually large and unusually small detection statistics separately, the relevant probability density function and distribution function can be achieved. In the third chapter, concerning the specialty of normal distribution, the detection statistics of several kinds of unusually large and unusually small data are constructed. The critical value tables applied in such statistic detection of outlying observations is introduced and the relevant large sample approximate distribution is discussed. In the fourth chapter, for extreme value distribution, Weibull distribution and other conventional distribution population, the detection statistic of unusually large data is constructed and the large sample approximate distribution is investigated.In the fifth chapter, the parameter estimation of incomplete observational data based on normal distribution and exponential distribution is investigated. Moreover, for the extra-incomplete observational data, the confidence interval method is discussed in detail. The pivot variables applied in confidence interval estimation of parameter are deduced by using any two of the order statistics of a complete sample. Thus, the distribution function and probability density function of the pivot variable can be achieved and the approximate confidence interval of large sample can be also obtained.Finally, in the sixth chapter, the robust stability of large-scale differential systems with uncertain parameters and delays is discussed. Applying the stabilizing local state feedback to each subsystem, making use of the method of Lyapunov function, and combining the method of inequality analysis, some sufficient conditions for BIBO stability and robust global uniform asymptotic stability of the large-scale systems are given.