Sampled‐data output feedback stabilization for a class of p‐norm switched stochastic nonlinear systems

Abstract

This paper addresses the sampled-data output feedback stabilization problem for a class of p-norm switched stochastic nonlinear systems with uncontrollable and unobservable linearizations around the origin. With sampled measurements, a reduced-order observer is constructed to estimate the unmeasurable states. Based on adding a power integrator technique and the homogeneous domination approach, a sampled-data output feedback controller is designed. Subsequently, by choosing an appropriate Lyapunov-Krasoviskii functional combined with stochastic analysis techniques, it is shown that the closed-loop system is globally asymptotically stable in probability under the proposed controller with a proper sampling period. Finally, two examples are presented to illustrate the effectiveness of the proposed scheme.

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

“…Remark Compared with the existing sampled‐data stabilization results for the deterministic nonlinear systems, such as, 5‐16,42,43 one difficult in this investigation lies in handling the high‐order Hessian terms (see (33), (34), (46), and (47)) generated by using the differential operator $$$ \ell $$$ in Definition 1, and another difficult lies in constructing the appropriate Lyapunov–Krasovskii functionals for the resulting closed‐loop system with input delays and stochastic disturbances under sampled‐data control (the Lyapunov function (52) for the corresponding closed‐loop system in this investigation was constructed differently from those in References 48 and 49 without considering the input delays). Furthermore, compared with the systems considered in References 5‐11 with non‐strict feedback structure, system (1) has the typical $$$ p $$$‐normal structure with stronger nonlinearities, therefore, we should use the nonlinear reduced‐order observer (9) to replace the linear full‐order observers constructed in References 5‐11 to estimate the unavailable states.…”

“…T . Now, we will handle the last term in the right-hand side of (48). By combining the system (8), the reduced-order observer (9), the coordinate transformation (10), the constructed virtual control laws and the designed sampled-data output feedback controller (24), the resulting closed-loop stochastic nonlinear system can be further represented as…”

Global adaptive output feedback control for a class of stochastic nonlinear systems with unknown homogeneous growth rates

“…Lemma [18] Let be positive constants. Given any real‐valued function , the following inequality holds : …”

“…Since stochastic factors are avoidable and widely existing in real world, a great deal of efforts have been devoted into the stabilization problems for stochastic nonlinear systems, see References 12‐19 and the references therein. An sufficient condition to guarantee global output feedback stabilization for stochastic nonlinear continuous‐time systems was proposed in Reference 13.…”

Adaptive output feedback control for a class of switched stochastic nonlinear systems under event‐triggered mechanism

“…Switched systems, as a special type of hybrid systems, have attracted a great amount of attention [3][4][5]. At present, many effective methods have been presented to study the stability and stabilization of switched systems [6][7][8], such as the multiple Lyapunov functions (MLFs) method, the common Lyapunov function (CLF) method and the average dwell time (ADT) method. With the help of these methods, many significant achievements have been made.…”