Global stabilization for a class of upper‐triangular stochastic nonlinear systems with input delay via sampled‐data output feedback

Abstract

The contribution of this investigation lies in solving a sampled‐data output feedback stabilization problem for a class of upper‐triangular stochastic nonlinear systems in p$$ p $$‐normal structure with unavailable states and uncertain time‐varying input delay. A reduced‐order observer with the available sampled output detection is developed for the focused system to estimate its unavailable states, and under such observer, a sampled‐data output feedback stabilizer is constructed by combining the backstepping and adding a power integral techniques. Through selecting the appropriate Lyapunov–Krasovskii functionals, we can demonstrate that the adverse influences caused by the uncertain time‐varying delays in the resulting closed‐loop system can be restricted effectively by the constructed stabilizer, and further, by following the stochastic differential theories, the global stability of the considered resulting closed‐loop system can be analyzed under the suitable design parameters and allowable sampling period. Finally, two examples are given to verify the effectiveness of the proposed control method.

Reduced‐order observer‐based finite‐time control for one‐sided Lipschitz nonlinear switched singular systems

“…Meanwhile, [14] gave the design of reduced-order observer using the generalized Sylvester equations, but it did not fully utilize some of the state information that can be measured. The reduced-order observer with the available detected sampled output measurement was constructed to estimate the unavailable states of the considered systems in [19,25]. However, in this paper, by using coordinate equivalent transformation for system (1), the measurable states and the unmeasurable states are successfully separated, and then a dynamic system for error estimation of the unmeasurable states is designed.…”

“…In order to facilitate the simulation, take the initial value as E 1c η(0) = [ 0.11 0.20 0 0.26 ] T and disturbance input 𝜔(t) = 0.5 √ cos(t). According to (17) and (19) yields…”

“…The dynamic output feedback controller can solve the stabilization problem when the states are completely unavailable. But in actual systems, the state information usually can be detected, to this end, several methods have been proposed in the literatures, such as sliding mode observer based on coordinate equivalent transformation, 12 unknown input observer (UIO) designed by using the linear matrix inequality approach, 13,23 Luenberger observers based on the generalized Sylvester equations, 14 the reduced-order observer with the detected sampled output measurement, 19,25 and so forth. Therefore, the state observer is introduced to construct a controller.…”

“…And Reference 18 explored the design of reduced‐order filters for NSS with global Lipschitz conditions. The stabilization for a class of upper‐triangular stochastic nonlinear systems satisfying the locally Lipschitz condition was investigated in Reference 19. It should be pointed out that above results were given under Lipschitz conditions which are conservative.…”

Fuzzy observer design for sampled nonlinear systems with measurement uncertainty

“…The third approach is continuous-discrete design, that is, measured outputs are directly applied to design a continuous observer [18][19][20][21]. Moreover, the problem of sampled-data output feedback stabilization was addressed for nonlinear systems with input delay in [22,23]. However, for a real physical system, its measured outputs are inevitably affected by the sensor and the external environment.…”