Simultaneous stabilization of single-input nonlinear systems with bounded controls

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Summary In this paper, the problem of simultaneous stabilization in probability by state feedback is investigated for a class of stochastic nonlinear systems whose drift and diffusion terms are dependent on the control and for which classical methods are not applicable. Under the assumption that a collection of stochastic control Lyapunov functions (SCLFs) is known and based on the generalized stochastic Lyapunov theorem, we derive sufficient conditions for the simultaneous stabilization in probability by a continuous state feedback controller that we explicitly compute. We also derive a necessary condition when the system coefficients satisfy some regularity conditions. This work generalizes previous results on the simultaneous stabilization of stochastic nonlinear systems. The obtained results are illustrated by a numerical example.

Section: Main Results: Design Methods Of Simultaneously Stabilizing C...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the simultaneous stabilization of stochastic nonlinear systems

Himmi

Oumoun

2022

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“…However, many of the previous studies (see, e.g., previous works [8][9][10][11]) have focused on linear systems. For the nonlinear systems, the literature has included very few results [1,[12][13][14]. The CLF is one of the well-established existing techniques for the stabilization of nonlinear systems, simultaneously [1].…”

Section: Introductionmentioning

confidence: 99%

Simultaneous stabilization of nonlinear systems with different and multiple time‐varying delays

Dastaviz

Binazadeh

2022

The simultaneous stabilization is addressed for a collection of nonlinear systems with multiple time‐varying delays. The time delays vary not only from one system to the other but even from one state to another within a system. The nonlinear functions may also be different for each system of the collection. A delay‐independent simultaneously stabilizing control law is presented by developing a Control Lyapunov‐Krasovskii Functional (CLKF) method. This controller has a unified structure for all the systems and, despite differences in nonlinearities and delays, leads to the stabilization of all the systems, simultaneously. During the design procedure, first, a systematic approach is provided to construct a CLKF of a particular form for each system. Second, a simultaneously stabilizing control law is defined based on the constructed CLKFs. Finally, a practical example is given to verify the efficiency and applicability of the given method.

“…Therefore, the investigation of simultaneous stabilization problems is quite relevant from a practical point of view, and many important results have been obtained for linear systems: see [21][22][23][24][25] and references therein. For nonlinear systems, the problem is more involved, and there are fewer results in the literature, for example, [26][27][28][29][30]. All these works deal with the simultaneous stabilization of linear and nonlinear deterministic systems.…”

Section: Introductionmentioning

confidence: 99%

Continuous simultaneous stabilization of single‐input nonlinear stochastic systems

Iggidr

Oumoun

Souza

2020

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This paper investigates the simultaneous stabilization of a collection of continuous single‐input non‐linear stochastic systems, with coefficients that are not necessarily locally Lipschitz. A sufficient condition for the existence of a continuous simultaneously stabilizing feedback control is proposed — it is based on the generalized stochastic Lyapunov theorem and on the technique of stochastic control Lyapunov functions. This condition is also necessary, provided that the system's coefficients satisfy some regularity conditions. Moreover, the proposed feedback can be chosen to be bounded under the assumption that appropriate control Lyapunov functions are known. All the proposed simultaneously stabilizing state feedback controllers are explicitly constructed. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed approach.