| In this dissertation, a kind of linear time invariant systems with unmodeled dynamics and nonlinear uncertainties are considered by using backstepping approach and variable structure control algorithm. Also another kind of linear time varying systems are studied based on the same method. Meanwhile, the problem of variable structure robust observer design for a kind of uncertain systems is also considered in this paper. The main contents include three parts:In the first part, the minimum phase systems with unmodeled dynamics and disturbances in the input-output channel are studied . Emelyanov. S. V (1998) studied the output feedback problem for the uncertain systems with exact linear model and constructed robust variable structure observer using descending-order observer method. For the same model but assuming that the parameters of the linear parts unknown, Wu yuqiang and Xinghuo Yu(1998) proposed a kind of new robust adaptive variable structure controller design algorithm. Its defect is the algorithm becomes very complex when the relative degree exceeds two.As we all know, backstepping approach completely solves the controller design problem of parametric-strict-feedback systems. For a large scale of linear time- invariant systems, linear time-varying systems and nonlinear systems, many scholars proposed a series of new schemes. In addition, there are many people presented a kind of new control design scheme by the combination of backstepping approach and softied-variable control scheme.For a kind of dynamic uncertain systems, basing on backstepping scheme and combining variable structure and nonlinear damping approach, this paper sufficiently considers unmodeled dynamics and disturbances in the input-output channel. And presents a kind of new globally stabilizing nonlinear controller design scheme only using input and output signals, which guarantees the boundness of all the signals in the closed system. The output can be made sufficiently small by properly choosing the controller parameters and the intermediate control functions. The controller is easy to be carried out, and the assumptions can be weaker compared to other works.The second part deals with the problem of output tracking for a kind of linear time-varying uncertain systems described by transfer functions. For the continuous minimum phase system, Narendra (1978, 1980) presented globally stabilized model reference adaptive control scheme, which later became a kind of generic design method of robust adaptive control. On the base of Narendra' s work, in order to suppress the unmodeled dynamics and external disturbances, many robust adaptive control schemes are proposed. In choosing control structures, Morse (1990, 1992) proposed a kind of unifying method of theparameter adaptive control. For the linear plants, he also proved that a designed well equivalent controller could lead to a tunable closed loop parametric system that can be stabilized. Basing on the tuning theory, Morse (1992) proposed a kind of switching parametric adaptive control scheme and proved that a tunable closed loop system can be globally stabilized. What' s more, the tracking error can be driven to zero. In addition, Morse proved that tenable system must be a minimum phase system. For linear time varying systems, Tskalis and loannou (1992,1989) proposed MRAC design method. However all these design schemes based on the linear control structure. When the relative degree exceeds one, the controller' s design and the stability analysis of the closed system becomes very difficult.Using the cogent validity of backstepping' s solving parametric-strict-feedback nonlinear systems, Xinghuo Yu and Wu Yuqiang (1998) solved the output-tracking problem of a kind of linear time varying system by combining nonlinear damping method and variable structure scheme. In this dissertation, we sufficiently consider the effect of disturbances in the input channel basing on the same model. By the proper choices of the controller parameters and the intermediate control fu...
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