Input‐output finite‐time stabilisation of linear systems with input constraints

Amato, Francesco; Carannante, G.; Tommasi, G. De; Pironti, A.

doi:10.1049/iet-cta.2014.0160

Cited by 27 publications

(12 citation statements)

References 20 publications

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“…In this section, we recall two control techniques, namely the constrained

{scriptH}_{\infty}

control [18] and the S‐IO‐FTS [19], which will be exploited later in Section 4 to design the proposed control system for lateral collision avoidance.…”

Section: Constrained Control Techniquesmentioning

confidence: 99%

Hybrid architecture for vehicle lateral collision avoidance

Ariola

Tommasi

Tartaglione

et al. 2018

IET Control Theory & Applications

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“…In this section, we recall two control techniques, namely the constrained

{scriptH}_{\infty}

control [18] and the S‐IO‐FTS [19], which will be exploited later in Section 4 to design the proposed control system for lateral collision avoidance.…”

Section: Constrained Control Techniquesmentioning

confidence: 99%

Hybrid architecture for vehicle lateral collision avoidance

Ariola

Tommasi

Tartaglione

et al. 2018

IET Control Theory & Applications

Self Cite

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“…Since we want to force disjoint constraints for the cart displacement and for the pendulum angle, we consider separately the two components of the output z, and we extend the proposed approach to the structured IO-FTS, as it has been done in [6]. To this aim, we consider the two outputs z 1 = C z 1 x = s and z 2 = C z 2 x = , and we replace inequality (27c) with the following two inequalities:…”

Section: Case Study: Quadratic Io-fts With An  ∞ Bound Of An Invementioning

confidence: 99%

“…with > 0, it is also possible to add a constraint on the control input (more details can be found in [6]). in Ω, when the disturbance is such that ‖w‖ 2,R ≤ 1.…”

Section: Case Study: Quadratic Io-fts With An  ∞ Bound Of An Invementioning

confidence: 99%

“…Since we want to force disjoint constraints for the cart displacement and for the pendulum angle, we consider separately the two components of the output z , and we extend the proposed approach to the structured IO‐FTS, as it has been done in . To this aim, we consider the two outputs

z_{1} = C_{z_{1}} x = s

and

z_{2} = C_{z_{2}} x = φ

, and we replace inequality with the following two inequalities:

\begin{array}{l} ((), \begin{matrix} arrayleft \\ Π & Π C_{z_{1}}^{T} \\ C_{z_{1}} Π & q_{1}^{- 1} \end{matrix}) > 0, & ((), \begin{matrix} arrayleft \\ Π & Π C_{z_{2}}^{T} \\ C_{z_{2}} Π & q_{2}^{- 1} \end{matrix}) > 0 . \end{array}

Moreover, by adding to the feasibility problem in Theorem the inequality

(\begin{array}{l} Π & L^{T} \\ L & υ^{- 1} \end{array}) > 0,

with υ > 0, it is also possible to add a constraint on the control input (more details can be found in ).…”

Section: Case Study: Quadratic Io‐fts With An H∞ Bound Of An Invertedmentioning

confidence: 99%

See 1 more Smart Citation

The Mixed Robust /FTS Control Problem Analysis and State Feedback Control

Amato¹,

Cosentino²,

Tommasi³

et al. 2015

Asian Journal of Control

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In this paper we deal with the mixed  ∞ /finite-time stability control problem. More specifically, given an open loop uncertain linear system, we provide a necessary and sufficient condition for quadratic input-output finite-time stability with an  ∞ bound. Exploiting this result we also give a sufficient condition to solve the related synthesis problem via state-feedback. The property of quadratic input-output finite-time stability with an  ∞ bound implies that the system under consideration satisfies an  ∞ performance bound between the disturbance input and the controlled output and, at the same time, is input-output finite-time stable for all admissible uncertainties. This condition requires the solution of a feasibility problem constrained by a pair of differential linear matrix inequalities (LMIs) coupled with a time-varying LMI. The proposed technique is illustrated by means of both a numerical and a physical example.

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“…In the last decade, we have witnessed an increasing interest in the problem of finite‐time stability and control for linear time‐delay systems . The finite‐time stability (FTS) introduced in means that the state of a system does not exceed some bound during a fixed interval time.…”

Section: Introductionmentioning

confidence: 99%

Robust Finite‐Time Control for Linear Time‐Varying Delay Systems With Bounded Control

Niamsup

Phát

2016

Asian Journal of Control

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This paper develops a novel finite-time control design for linear systems subject to time-varying delay and bounded control. Based on the Lyapunov-like functional method and using a result on bounding estimation of integral inequality, we provide some sufficient conditions for designing state feedback controllers that guarantee the robust finite-time stabilization with guaranteed cost control. The conditions are obtained in terms of linear matrix inequalities (LMIs), which can be determined by utilizing the Matlab LMI Control Toolbox. A numerical example is given to show the effectiveness of the proposed method.whereM 12,12 = −0.5I, M 10,10 = − 1 1 + 27r 2 b 4 I, M 44 = −8S 3 + Q 2 , M 11,11 = − 1 , M 88 = M 99 = −12S 3 , M 12 = −2X 1 , M 13 = −2X 2 , M 14 = PD, M 16 = 6X 1 , M 45 = D T S 4 , M 1i = 0, i = 8, 9, 12, M 1,10 = P, M 1,11 = PB, M 15 = A ⊤ S 4 , M 24 = −2S 3 , M 26 = 6X 1 , M 28 = 6S 3 , M 2i = 0, i = 3, 5, 7, 9, 10, 11, 12, M 34 = −2S 3 , M 39 = 6S 3 , M 3i = 0, i = 5, 6, 8, 10, 11, 12, M 4i = 0, i = 6, 7, 10, 11, 12, M 48 = M 49 = 6S 3 , M 5i = 0, i = 6, 7, 8, 9, 10, 11, M 5,12 = S 4 ,

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Input‐output finite‐time stabilisation of linear systems with input constraints

Cited by 27 publications

References 20 publications

Hybrid architecture for vehicle lateral collision avoidance

Hybrid architecture for vehicle lateral collision avoidance

The Mixed Robust /FTS Control Problem Analysis and State Feedback Control

Robust Finite‐Time Control for Linear Time‐Varying Delay Systems With Bounded Control

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