Stability analysis for a class of nonlinear discrete-time control systems subject to disturbances and to actuator saturation

Oliveira, M. Z.; Silva, J.M. Gomes da; Coutinho, Daniel

doi:10.1080/00207179.2013.765036

Cited by 8 publications

(6 citation statements)

References 9 publications

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“…It was already shown by Coutinho et al 24 that the class of rational systems, in the continuous‐time domain, can be represented in a Differential‐Algebraic Representations form. Similarly, this representation could be used in the context of discrete‐time systems, as also presented in the literature 13,32,48 . Thus, from Assumption 1, system (1) can be recast as

\begin{align} x_{k + 1} & = A_{1} false(x_{k}, δ_{k} false) x_{k} + A_{2} false(x_{k}, δ_{k} false) π_{k} + A_{3} false(x_{k}, δ_{k} false) sat false(u_{k} false) + A_{4} false(x_{k}, δ_{k} false) w_{k}, \\ 0 & = {normalΩ}_{1} false(x_{k}, δ_{k} false) x_{k} + {normalΩ}_{2} false(x_{k}, δ_{k} false) π_{k} + {normalΩ}_{3} false(x_{k}, δ_{k} false) sat false(u_{k} false) + {normalΩ}_{4} false(x_{k}, δ_{k} false) w_{k}, \\ z_{k} & = C_{1} false(x_{k}, δ_{k} false) x_{k} + C_{2} false(x_{k}, δ_{} \end{align}

…”

Section: Problem Formulationmentioning

confidence: 99%

“…The use of Differential and Difference‐Algebraic Representations in analysis and control of nonlinear systems has been investigated in the last decades, under several aspects in the context of local stability analysis, 28,31‐34 local stabilization and DOA estimation, 12,13,35‐37 local stabilization and output performance, 12,24 filters and observers, 26,38,39 anti‐windup design, 40,41 event‐triggered control, 42 and more recently for the output regulation problem 43 . In the context of stability analysis, less‐conservative results to nonlinear systems described in a DAR form were obtained by searching for polynomial and rational Lyapunov candidate functions 31,44,45 .…”

Section: Introductionmentioning

confidence: 99%

“…Secondly the approach is adapted to the problem of estimating the largest DOA, disregarding the presence of exogenous disturbances. To the best of the authors' knowledge, Oliveira et al 32,48 proposed analysis conditions to constrained nonlinear systems described by DAR to investigate both problems, but without providing synthesis conditions. Klug et al 25 also investigated similar problems for systems represented as Takagi–Sugeno models with nonlinear consequent, but without taking into account time‐varying parameters or control input saturation.…”

Section: Introductionmentioning

confidence: 99%

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Gain‐scheduled control design for discrete‐time nonlinear systems using difference‐algebraic representations

Reis

Araujo

Tôrres

et al. 2020

Intl J Robust & Nonlinear

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Summary This paper addresses the local stabilization problem of nonlinear systems described by Difference‐Algebraic Representations (DAR). A novel set of sufficient Linear Matrix Inequalities (LMI) conditions are developed to design gain‐scheduled state feedback controllers. The proposed approach uses parameter‐dependent Lyapunov functions and new auxiliary decision variables aiming to obtain less conservative results. Two optimization problems are proposed to either obtain the largest estimated Domain‐of‐Attraction (DOA) or minimize the ℓ2‐gain from the energy‐bounded disturbance input to the performance output. Furthermore, this investigation considers control input saturation and system states constrained in a polyhedral region. Numerical examples are provided to illustrate the effectiveness of the proposed methodology, showing favorable comparisons with recently published similar approaches.

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\begin{align} x_{k + 1} & = A_{1} false(x_{k}, δ_{k} false) x_{k} + A_{2} false(x_{k}, δ_{k} false) π_{k} + A_{3} false(x_{k}, δ_{k} false) sat false(u_{k} false) + A_{4} false(x_{k}, δ_{k} false) w_{k}, \\ 0 & = {normalΩ}_{1} false(x_{k}, δ_{k} false) x_{k} + {normalΩ}_{2} false(x_{k}, δ_{k} false) π_{k} + {normalΩ}_{3} false(x_{k}, δ_{k} false) sat false(u_{k} false) + {normalΩ}_{4} false(x_{k}, δ_{k} false) w_{k}, \\ z_{k} & = C_{1} false(x_{k}, δ_{k} false) x_{k} + C_{2} false(x_{k}, δ_{} \end{align}

…”

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Gain‐scheduled control design for discrete‐time nonlinear systems using difference‐algebraic representations

Reis

Araujo

Tôrres

et al. 2020

Intl J Robust & Nonlinear

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show abstract

“…Compared with linear systems with AS, it is worth noticing that there are few significant results for nonlinear systems with AS. The backstepping technique was used in to investigate the adaptive control of nonlinear systems with AS, and a modified version of the generalised sector bound condition was considered in to deal with the saturation nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

“…This work was supported by the National Nature Science Foundation of China (NSFC) (61573218, 61174036) and the Major International (Regional) Joint Research Project of the National Nature Science Foundation of China (61320106011). a modified version of the generalised sector bound condition was considered in [6] to deal with the saturation nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

Stabilization and H_∞ Control of Nonlinear Switched Hamiltonian Systems Subject to Actuator Saturation

Han

Wei

2016

Asian Journal of Control

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This paper investigates the stabilization and H∞ control problem of nonlinear switched Hamiltonian systems (NSHSs) subject to actuator saturation (AS) under arbitrary switching paths. First, based on the saturating actuator property, an appropriate state feedback is designed under a realistic assumption for the stabilization of NSHSs with AS. Then, an H∞ controller is designed for NSHSs subject to AS with external disturbances in order to attenuate the disturbances. Futhermore, the results obtained for NSHSs are applied to study the stabilization and H∞ control of switched nonlinear systems with AS via the Hamiltonian realization method. Finally, simulation examples show the efficiency of the methods and results proposed in this paper.

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On the ℓ2-stability of time-varying linear and nonlinear discrete-time MIMO systems

Venkatesh

2014

Control Theory Technol.

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Stability analysis for a class of nonlinear discrete-time control systems subject to disturbances and to actuator saturation

Cited by 8 publications

References 9 publications

Gain‐scheduled control design for discrete‐time nonlinear systems using difference‐algebraic representations

Gain‐scheduled control design for discrete‐time nonlinear systems using difference‐algebraic representations

Stabilization and H_∞ Control of Nonlinear Switched Hamiltonian Systems Subject to Actuator Saturation

On the ℓ2-stability of time-varying linear and nonlinear discrete-time MIMO systems

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Stability analysis for a class of nonlinear discrete-time control systems subject to disturbances and to actuator saturation

Cited by 8 publications

References 9 publications

Gain‐scheduled control design for discrete‐time nonlinear systems using difference‐algebraic representations

Gain‐scheduled control design for discrete‐time nonlinear systems using difference‐algebraic representations

Stabilization and H∞ Control of Nonlinear Switched Hamiltonian Systems Subject to Actuator Saturation

On the ℓ2-stability of time-varying linear and nonlinear discrete-time MIMO systems

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Stabilization and H_∞ Control of Nonlinear Switched Hamiltonian Systems Subject to Actuator Saturation