Stability, Controllability and Observability are three principal properties of control systems,and the theory about them is main basis of control theory. Several problems in control theory relative to stability,Controllability and Observability are studied in the dissertation,and they are respectively : (1) relationships between controllability with observability of a multivariable linear time-invariant system and controllability with observability of its corresponding discrete system; (2) stability of linear interval systems; (3) controllability and observability of linear interval systems; (4) global asymptotic stability of nonlinear autonomous systems; (5) conditions that continuous nonlinear systems don't wander in (on) a given domain; and (6) estimation of attraction domains of equilibrium points of a continuous nonlinear system. Concrete research contents and results which have been gotten on six problems mentioned above are as follows : (1) Revealing several useful relationships in linear system theory ,and presenting sufficient and necessary conditions that all states of a linear time--invariant system are controllable,observable, or both controllable and observable, and all states of its corresponding discrete system are also controllable, observable ,or both controllable and observable. (2) Studying stability of linear interval systems by the method of interval analysis. Giving Routh criterion of interval and methods analyzed Hurwitz property of an interval polynomial by using of Routh criterion of interval. Giving analytic methods for Schur property of a discrete interval polynomial. Presenting the determinant definition and the computational formula of an interval matrix. Presenting definitions of a characteristic interval matrix and a characteristic interval polynomial, and methods translated a characteristic interval polynomial into an interval polynomial. And presenting necessary conditions and sufficient conditions judging a linear interval system to be stable by using of Routh criterion of interval. (3) Studying controllability and observability of a linear interval system by means of the theory of an interval matrix's rank and its determinant, and getting necessary conditions that a linear interval system is controllable, or observable, and sufficient and necessary conditions where linear interval systems are special ones. Giving controllable standard forms, observable standard forms, and both controllable and observable standard forms of linear interval systems. (4) Presenting one global asymptotic stability theorem which equals to Krasovskii's ones, and on the basis of that, presenting several new results on global asymptotic stability of nonlinear autonomous systems. (5) Presenting definitions of wanderings and conditions that wanderings are inexistent of a continuous nonlinear system in (on) a given domain. By these conditions, not only a system's closed loci,limit cyc
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