• International Journal of Control, Automation, and Systems
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• v.6 no.6
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• pp.859-872
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• 2008

In this paper, the problem of partial asymptotic stabilization of nonlinear control cascaded systems with integrators is considered. Unfortunately, many controllable control systems present an anomaly, which is the non complete stabilization via continuous pure-state feedback. This is due to Brockett necessary condition. In order to cope with this difficulty we propose in this work the partial asymptotic stabilization. For a given motion of a dynamical system, say x(t,$x_0,t_0$)=(y(t,$y_0,t_0$),z(t,$z_0,t_0$)), the partial stabilization is the qualitative behavior of the y-component of the motion(i.e., the asymptotic stabilization of the motion with respect to y) and the z-component converges, relative to the initial vector x($t_0$)=$x_0$=($y_0,z_0$). In this work we present new results for the adding integrators for partial asymptotic stabilization. Two applications are given to illustrate our theoretical result. The first problem treated is the partial attitude control of the rigid spacecraft with two controls. The second problem treated is the partial orientation of the underactuated ship.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.67 no.2
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• pp.261-269
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• 2018

In this paper, we propose a Takagi-Sugeno (T-S) fuzzy-model-based design for the tracking control of a class of nonlinear underwater glider. By using the partial linearization and the sector nonlinearity, the underwater glider with six degrees of freedom (6 DOF) is modelled by the T-S fuzzy model. The concerned tracking control problem with $H_{\infty}$ performance is converted into the stabilization one for the error dynamics between the given nonlinear underwater glider and the reference time-varying input. Sufficient conditions are derived for the asymptotic stabilizability of the error dynamics in the format of matrix inequality. Simulation results demonstrate the effectiveness of the proposed design methodology.