&lt;tex&gt;$H_infty$&lt;/tex&gt;Control for Discrete-Time Nonlinear Stochastic Systems

Berman, N.; Shaked, U.

doi:10.1109/tac.2006.876808

Cited by 72 publications

(36 citation statements)

References 13 publications

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“…To design the controller (15), matrix inequality (15) must be solvable and matrix inequality (15) in Theorem 4 must be inverted into LMI form. In the following section, we will find a way for the solution of (15).…”

Section: Resultsmentioning

confidence: 99%

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RobustH∞Control for Discrete-Time Stochastic Interval System with Time Delay

Chen

Shen

2013

Mathematical Problems in Engineering

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The robust ∞ control problem for discrete-time stochastic interval system (DTSIS) with time delay is investigated in this paper. The stochastic interval system is equivalently transformed into a kind of stochastic uncertain time-delay system firstly. By constructing the appropriate Lyapunov-Krasovskii functional, the sufficient conditions for the existence of the robust ∞ controller for DTSIS are obtained in terms of linear matrix inequality (LMI) form, and the robust ∞ controller is designed. Finally, a numerical example with simulation is given to show the effectiveness and correctness of the designed robust ∞ controller.

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Section: Resultsmentioning

confidence: 99%

“…Meanwhile, from Hinrichsen who presented the ∞ control problems for stochastic systems in 1998 [9], more and more experts begin to study the stochastic ∞ control problems [10][11][12][13][14][15][16][17]. In the view of dissipation, Berman develops a ∞ -type theory for a large class of time-continuous stochastic nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

RobustH∞Control for Discrete-Time Stochastic Interval System with Time Delay

Chen

Shen

2013

Mathematical Problems in Engineering

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“…Originated in Reference , the theory of dissipative systems has been playing a vital role in the analysis and synthesis of dynamical systems (see References for some publications concerning linear system and References for nonlinear systems). It is worth mentioning that although there have been certain initial research work on dissipative control for nonlinear MJSs, the system dynamics under investigation are described either by linear systems with simple additive nonlinear disturbances or by linearized ones after certain approximated manipulations (eg, T‐S fuzzy approach) techniques.…”

Section: Introductionmentioning

confidence: 99%

Dissipative control for nonlinear Markovian jump systems with mixed time‐delays: The discrete‐time case

Fang

Yuan

et al. 2020

Intl J Robust & Nonlinear

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This article is concerned with the dissipative control problem for discrete-time nonlinear Markovian jump systems subject to both discrete and distributed time-delays. The purpose is to design a state feedback controller that is capable of guaranteeing the required closed-loop stability and dissipativity performances simultaneously. By resorting to Lyapunov functional methodology and completing square technique, sufficient conditions are established for the existence of the desired state feedback controller in terms of certain Hamilton-Jacobi inequalities (HJIs). Within the provided framework, the required controller parameters can be obtained by solving the corresponding HJIs. Finally, two numerical simulation examples are presented to demonstrate the correctness and effectiveness of the developed control paradigm. K E Y W O R D S dissipative control, Hamilton-Jacobi inequality, mixed time-delays, nonlinear Markovian jump systems 1 Int J Robust Nonlinear Control. 2020;30:2871-2888.wileyonlinelibrary.com/journal/rnc

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“…For several decades, stochastic control and nonlinear control are arguably two of the most active research areas in systems and control, and many different kinds of nonlinear stochastic systems have been investigated in the literature, see [3], [11], [17], [18], [20], [27] and the references therein. Among various descriptions of nonlinearities, the so-called stochastic nonlinearities characterized by statistical moments has gained particular attention since they encompass several well-studied nonlinearities in stochastic systems [16].…”

Section: Introductionmentioning

confidence: 99%

“…It should be noted that in a recent paper [3] a small-gain theorem for large-scale systems under the presence of time-delays has been presented. In contrast to [1] it does not explicitly take into account multiple communication channels.…”

Section: Introductionmentioning

confidence: 99%

Robust ${\cal H}_{\infty}$ Finite-Horizon Control for a Class of Stochastic Nonlinear Time-Varying Systems Subject to Sensor and Actuator Saturations

Wang

Dong

et al. 2010

IEEE Trans. Automat. Contr.

146

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Abstract-This technical note addresses the robust finite-horizon output feedback control problem for a class of uncertain discrete stochastic nonlinear time-varying systems with both sensor and actuator saturations. In the system under investigation, all the system parameters are allowed to be time-varying, the parameter uncertainties are assumed to be of the polytopic type, and the stochastic nonlinearities are described by statistical means which can cover several classes of well-studied nonlinearities. The purpose of the problem addressed is to design an output feedback controller, over a given finite-horizon, such that the disturbance attenuation level is guaranteed for the nonlinear stochastic polytopic system in the presence of saturated sensor and actuator outputs. Sufficient conditions are first established for the robust performance through intensive stochastic analysis, and then a recursive linear matrix inequality (RLMI) approach is employed to design the desired output feedback controller achieving the prescribed disturbance rejection level. Simulation results demonstrate the effectiveness of the developed controller design scheme.

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<tex>$H_infty$</tex>Control for Discrete-Time Nonlinear Stochastic Systems

Cited by 72 publications

References 13 publications

RobustH∞Control for Discrete-Time Stochastic Interval System with Time Delay

RobustH∞Control for Discrete-Time Stochastic Interval System with Time Delay

Dissipative control for nonlinear Markovian jump systems with mixed time‐delays: The discrete‐time case

Robust ${\cal H}_{\infty}$ Finite-Horizon Control for a Class of Stochastic Nonlinear Time-Varying Systems Subject to Sensor and Actuator Saturations

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