Design Of Robust Pulse Controller For Uncertain Singular Systems

Singular systems are a kind of dynamical systems of more general than normal systems and have widely applied background. This is why singular systems have attracted so much interest in recent years, and they have already been developed sufficiently. In practice, there are unknown disturb inputs, which means the existence of uncertain errors, so it's hard to set up an exact mathematics model for the controlled systems. Under such circumstances, uncertain generalized systems have been widely concerned. Over the years, the study of uncertain singular systems has been mainly on the class of the systems with uncertainty in the first-order coefficient matrix.The researches on the systems with uncertainty in the first-order derivative coefficient matrix are still very few. Based on the results of previous studies, this paper does some studies on such uncertain systems. The main tasks are as follows:(1) The development process, essence and background of singular systems are introduced. In addition, important conclusions and properties of singular systems are concluded and analyzed. After the introduction of the expressions of three feedback controllers, their impacts on the systems about controllability, observability, impulse controllability and impulse observability are aggregated. The status of the development about robust control on the uncertain singular systems is briefly described.(2) This paper focuses on the theory of regional pole analysis and constraints of the systems with uncertainty in the first-order derivative coefficient matrix. The range of disturbance and the derivative feedback controller which ensure the uncertain systems regular, no pulse and the finite poles in the given disk. In addition, an example is given to illustrate the results.(3) The concept of impulse margin and the results of robust impulse-eliminating theory are introduced. Robust impulse-eliminating of the systems with uncertainty in the first-order derivative coefficient matrix is focused in this paper. Sufficient condition and robust impulse controller are given which could make the systems have arbitrary impulse margin. If the condition does not meet, the upper bound of the impulse margin of the augmented system is given which is the low bound of the original system. Moreover, this theory is generalized to discrete systems. Sufficient condition and robust causality controller are given which could make the systems have arbitrary causality margin. If the condition does not meet, the low bound of the causality margin of the augmented system is given which is the low bound of the causality margin of the original system. In addition, some examples are given to illustrate the results.