| In practical engineering problems, the theories of the design and analysis of structures are always established on the basis of the definite mathematics models. However, there are always uncertain factors in the structural engineering practices, such as the inaccuracy of the measurement, the complexity of the structures or errors in manufacture, etc. When the structures are large and complex, the combination of the uncertainty can have some effect on the systems. Therefore, it is necessary to design and analyze the structures with uncertain models directly.The uncertainty can be described as following three kinds: 1.physical uncertainty. It is correlated to load, material and geometrical size. Generally speaking, the change of working conditions and the errors in manufacturing or installation can bring this kind of uncertainty. 2.statistical uncertainty. Nowadays, probability statistical methods are used in solving uncertainty. But because there is no enough statistic information, samples cannot represent all the system information. 3.model uncertainty. During structural analysis and design, the models are constructed between the inputs, including load, geometric size and plastic modules, and the outputs, the displacement, stress and strain. Even beside the physical uncertainty, there are uncertainties in modeling such as the theoretical simplifying and unknown boundary conditions. Nowadays, during structural analysis and design, these uncertainties need be quantified by some uncertain methods. Generally speaking, according to the mathematical models with uncertainties, there are some models as follows: probability models, where uncertainties are described as random or probability variables; fuzzy models, which use the fuzzy statistic to describe uncertainties by fuzzy variables or functions; Fuzzy optimizations can draw conclusions in fuzzy field in design dimensions; convex models, which can, with certain sets (such as ellipsoid), describe those uncertainties by many convex optimizations; interval models, which use the interval variables to represent uncertainties and get interval analysis to solve them. The most common methods for solving uncertainty problems are to model the structural parameters as a random vector. At present dissertation, the random model is used to deal with the control problems of systems with uncertain parameters. The uncertainties of structural parameters are described by a random vector. And using the perturbation theory, the standard deviations of eigenvalues and responses of closed-loop systems with uncertain parameters are discussed. The method presented in this dissertation will not require the distribution function of the random parameters of the systems other than their means and variances. Similarly, the distribution function of random eigenvalues and responses will not be computed other than their means and variances. The robustness of stability and response, and the controllability of repeated mode are discussed. There are some details as follows:The vibration control problems of systems with uncertain parameters are discussed, which is approximated with the corresponding deterministic one. The uncertain parameters are modeled to be random variables. The formulas for calculating the standard deviations of eigenvalues of closed-loop systems are derived with the random model and the perturbation. The upper and lower bounds of eigenvalues of closed-loop systems with uncertain parameters is estimated. The robustness of stability for closed-loop systems is discussed. The affected response due to uncertain parameters of systems are discussed. The formulas for calculating the standard deviations of response of closed-loop systems are derived with the random model and the perturbation. The standard deviations of response can be used to estimate errors of that. The response robustness is discussed..The controllability of uncertain systems with repeated eigenvalues is discussed. The singular values of repeated modal control matrix was used deal with th...
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