Stability of adaptively stabilized stochastic systems

The sliding-mode control of nonlinear uncertain systems with un-modeled first-order actuator dynamics has been considered. A 2-SMC scheme with adaptive switching rule has been proposed, and its effectiveness has been shown for a class of systems encompassing non zero-input-stable (ZIS) systems and non-BIBS stable plants. The proposed algorithm is easy to implement and therefore suited to being used in practice; it is also effective in counteracting the transient peaking phenomenon. REFERENCES [1] N. Atassi and H. Khalil, " A separation principle for the stabilization of a class of nonlinear systems, " IEEE Trans. Properties of a combined backstepping/second order sliding mode control algorithm for some classes of uncertain nonlinear systems, " IEEE Trans. Automat. Applications of a suboptimal dis-continuous control algorithm for uncertain second-order systems, " Int. [4] , " Chattering avoidance by second order sliding mode control, " IEEE Trans. Abstract—Stochastic adaptive stabilization usually leads to the bounded-ness of the average of squared output of the stabilized system, but gives no conclusion on stability of the resulting system. This note proves that adap-tively stabilized stochastic system in its steady state is truly stable in the conventional sense.