Results on finite‐time boundedness and finite‐time control of non‐linear quadratic systems subject to norm‐bounded disturbances

Bhiri, B.; Delattre, Cédric; Zasadzinski, Michel; Abderrahim, Kamel

doi:10.1049/iet-cta.2016.1434

Cited by 9 publications

(2 citation statements)

References 21 publications

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“…A powerful method for stabilizing nonlinear systems and monitoring trajectory is called backstepping control. The basic goal of backstepping is to achieve Lyapunov cascade stability in equivalent loops in a subsystem of order one, which endows them with robustness and asymptotic overall stability [66][67][68][69][70][71]. Another very well-known control method is sliding mode control, which is noted for its stability, short response times, and sensitivity to parameter fluctuations [72][73][74][75][76].…”

Section: Introductionmentioning

confidence: 99%

Hybrid Approach Control of Micro-Positioning Stage with a Piezoelectric Actuator

Ounissi¹,

Kaddouri²,

Abdessemed³

2022

JISC

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For a class of system with nonlinear hysteresis, this paper presents an adaptive hybrid controller based on the hybrid backstepping-sliding mode, and describes the controller analytically by the LuGre model. Both backstepping and the sliding mode techniques are based on the Lyapunov theory. Drawing on this common point, the authors developed a new controller combining the two control techniques with a recursive design. The design aims to achieve two effects: assuring the stability of the closed loop system, and improving the continuous performance of the tracking position trajectory. The performance of the proposed hybrid controller was verified by implementing the identified Piezo model. The results show that our controller can track the system output desirably with the reference trajectory.

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Section: Introductionmentioning

confidence: 99%

Hybrid Approach Control of Micro-Positioning Stage with a Piezoelectric Actuator

Ounissi¹,

Kaddouri²,

Abdessemed³

2022

JISC

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“…In particular, quadratic systems are often encountered in chemical reactors, electrical power systems [15], robotics [11] and biology [13]. More specifically, the domain of attraction (DA) problems are discussed in [3,7], finite-time stability and stabilisation problems arising in the design of optimal control strategies is considered in [20], a guaranteed cost control in [1,2], the sufficient conditions for finite-time boundedness and stabilisation of continuous-time quadratic systems are derived in [6].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Output Feedback Control of Discrete-Time Nonlinear Quadratic Systems with Stochastic Parametric Uncertainty and Missing Measurements

Shi¹

2019

EAJAM

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Finite-time dynamic output feedback control for a class of discrete-time nonlinear quadratic systems with stochastic parametric uncertainty, exogenous disturbance and missing measurements, modeled by a Bernoulli distributed stochastic variable, is considered and sufficient conditions for FTSB under a dynamic output feedback controller are provided. As a consequence, a sufficient condition for FTSS is derived. A numerical example demonstrates the effectiveness of the method.

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Robust Unknown Input Observer of Nonlinear Quadratic Systems With Application to Sensor Fault Estimation

Abdullah

2024

Intl J Robust & Nonlinear

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A robust unknown input observer (UIO) is designed for nonlinear quadratic systems (NQSs) affected by unknown input, disturbance, and noise. It is assumed that in this article the system states and their estimates are varying inside a hyper‐rectangle region of known vertices. Based upon satisfying the observer matching condition and the minimum phase condition (at every vertex of the hyper‐rectangle region of the system states and their estimates), a set of tractable linear matrix inequalities (LMIs) is derived for computing the design matrices of robust UIO. The design methodology of robust UIO is extended to NQSs affected by sensor fault, disturbance, and noise. By modeling the sensor fault as a system state with unknown sensor fault input, it is found that the observer matching condition is satisfied and only the minimum phase condition should be verified at every vertex of the hyper‐rectangle region of the system states and their estimates. Another set of tractable LMIs is derived to compute the design matrices of robust UIO, which simultaneously estimates the system's states and sensor faults. A practical example of a nonlinear quadratic Rössler circuit affected by sensor fault, disturbance, and noise is used to show the design steps and to verify the proposed robust UIO. Simulation results indicate the ability of the proposed robust UIO to simultaneously estimate the system's states and sensor faults of NQSs affected by disturbance and noise.

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Results on finite‐time boundedness and finite‐time control of non‐linear quadratic systems subject to norm‐bounded disturbances

Cited by 9 publications

References 21 publications

Hybrid Approach Control of Micro-Positioning Stage with a Piezoelectric Actuator

Hybrid Approach Control of Micro-Positioning Stage with a Piezoelectric Actuator

Dynamic Output Feedback Control of Discrete-Time Nonlinear Quadratic Systems with Stochastic Parametric Uncertainty and Missing Measurements

Robust Unknown Input Observer of Nonlinear Quadratic Systems With Application to Sensor Fault Estimation

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