Regional stabilization of nonlinear sampled-data control systems: A quasi-LPV approach

Palmeira, Alessandra Helena Kimura; Silva, João Manoel Gomes da; Flores, Jeferson Vieira

doi:10.1016/j.ejcon.2020.11.001

Cited by 12 publications

(3 citation statements)

References 23 publications

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“…Hence, provided that the initial state of system (1) belongs to this estimate, it is ensured that the trajectories of the closed‐loop system (1)–(7) converge to the origin

\forall {T}_k\in \left[{\mathcal{T}}_1,{\mathcal{T}}_2\right]

. Similar to Reference 37, general conditions to tackle this problem are presented in the next theorem.…”

Section: Looped‐functional Approachmentioning

confidence: 99%

Stability analysis of Lure systems under aperiodic sampled‐data control

Titton

Silva

Valmórbida

et al. 2023

Intl J Robust & Nonlinear

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This article deals with the stability analysis of Lure type systems through aperiodic sampled‐data control laws, where the nonlinearity is assumed to be both sector and slope restricted. The proposed method is based on the use of a new class of looped‐functionals, which depends on the nonlinearity and its slope, and on a generalized Lure type function, that is quadratic on both the states and the nonlinearity and has a Lure‐Postnikov integral term. On this basis, conditions in the form of linear matrix inequalities to certify global or regional asymptotic stability of the closed‐loop system are obtained. These conditions are then used in optimization problems for computing the maximum intersampling interval or the maximum sector bounds for which the stability of the sampled‐data closed‐loop system is guaranteed. Numerical examples to illustrate the results are provided.

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“…Hence, provided that the initial state of system (1) belongs to this estimate, it is ensured that the trajectories of the closed‐loop system (1)–(7) converge to the origin

\forall {T}_k\in \left[{\mathcal{T}}_1,{\mathcal{T}}_2\right]

. Similar to Reference 37, general conditions to tackle this problem are presented in the next theorem.…”

Section: Looped‐functional Approachmentioning

confidence: 99%

Stability analysis of Lure systems under aperiodic sampled‐data control

Titton

Silva

Valmórbida

et al. 2023

Intl J Robust & Nonlinear

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show abstract

“…However, to ensure the correct control implementation, one needs to guarantee that the closed-loop trajectories remain confined inside the region where the polytopic model is valid. 35,36 This issue can be solved by determining a guaranteed region of attraction estimation contained in the region of validity. Unfortunately, this aspect is neglected by the majority of papers on ETC of quasi-LPV or TS fuzzy models, a few exceptions are for instance.…”

Section: Introductionmentioning

confidence: 99%

“…These polytopic representations are useful to derive stability or synthesis conditions in terms of linear matrix inequalities (LMIs). However, to ensure the correct control implementation, one needs to guarantee that the closed‐loop trajectories remain confined inside the region where the polytopic model is valid 35,36 . This issue can be solved by determining a guaranteed region of attraction estimation contained in the region of validity.…”

Section: Introductionmentioning

confidence: 99%

Event‐triggered control of quasi‐LPV systems with communication delays

Coutinho

Moreira

Palhares

2022

Intl J Robust & Nonlinear

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This paper addresses the dynamic periodic event‐triggered control for local stabilization of nonlinear networked control systems with communication delays. Based on a polytopic quasi‐linear parameter‐varying (quasi‐LPV) model of the nonlinear plant and the Lyapunov–Krasovskii stability theory, a local stability analysis condition is established. Then a constructive co‐design condition is proposed to jointly design the state‐feedback control law and the trigger rule. The local asymptotic stability of the closed‐loop equilibrium point of interest is ensured with a guaranteed region of attraction where trajectories remain inside even in the presence of communication delays. An optimization procedure is proposed to perform the co‐design considering the objectives of enlarging the guaranteed region of attraction and reducing the number of transmissions. Numerical examples indicate a trade‐off between these two objectives. Also, the examples illustrate the effectiveness of the proposed dynamic event‐triggered control co‐design approach over both its static counterpart and periodic time‐triggering mechanisms.

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