Stability analysis and robust performance of periodic discrete-time uncertain systems via structured Lyapunov functions

Keles, Natália Augusto; Agulhari, Cristiano Marcos; Lacerda, Márcio J.

doi:10.1016/j.ejcon.2020.06.006

Cited by 4 publications

(6 citation statements)

References 20 publications

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“…Theorem 1: Assume that positive scalars η, , ρ i , υ i , ζ b , (b = 1, 2, 3, 4), T i and gain matrices K i (t), V i are known. The closed-loop UPPTVSs (7) and the configured error system (8) are asymptotically stable, if the matrices J i (t) > 0, Q i > 0, R 1 > 0, R 2 > 0 and R 3 > 0 (i ∈ N) exist, such that the below relation holds:…”

Section: Resultsmentioning

confidence: 99%

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Disturbance Observer-Based Robust Control Design for Uncertain Periodic Piecewise Time-Varying Systems With Disturbances

Thilagamani¹,

Sakthivel

Annalakshmi

et al. 2023

IEEE Access

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With the aid of disturbance observer strategy, this article aims to investigate the disturbance rejection and stabilization problems for periodic piecewise time-varying systems that are subject to timevarying delays, parameter uncertainties, nonlinear perturbations and exogenous disturbances. To be more specific, the periodic piecewise time-varying systems are built by segmenting the fundamental period of periodic systems into a limited number of subintervals. Further, the disturbances engendered from an exogenous system are estimated by deploying the disturbance observer and subsequently, on the premise of disturbance that is esimated, a robust controller protocol is constructed for the considered system. Moreover, by bridging the time-varying periodic piecewise Lyapunov-Krasovskii functional with a matrix polynomial lemma, a set of adequate criteria is framed, which confirms the asymptotic stability of the system that is being addressed. Subsequently, on the premise of established criteria, the design of periodic piecewise gain matrices of devised controller and configured observer are presented. Eventually, the importance and potential of the presented theoretical concepts are evidenced through offering a numerical illustration with the simulation results.INDEX TERMS Periodic piecewise time-varying systems, disturbance observer, uncertainity, nonlinear perturbations, time-varying delay.

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Section: Resultsmentioning

confidence: 99%

“…solutions [6], [7], [8]. In order to confront this difficulty, the periodic piecewise systems (PPSs) has been introduced, which aids in simplifying the analysis of the system and making dynamical results more accurate [9], [10].…”

Section: Introductionmentioning

confidence: 99%

Disturbance Observer-Based Robust Control Design for Uncertain Periodic Piecewise Time-Varying Systems With Disturbances

Thilagamani¹,

Sakthivel

Annalakshmi

et al. 2023

IEEE Access

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“…While, according to Remarks 1 and 6, we can also mechanically verify its GES via presetting the degrees of s i,11 , s i,11j , s i,12 , s i,12j , s i,21 , s i,21j , and V i,u (t, x) (i, j ∈ {1, 2}) to be 2, and then numerically obtaining the required uncertainty-dependent piecewise function V u ( 43)- (45). Via replacing u with u(⋅) and presetting the degrees of s i, 13 , s i,14 , s i, 22 , s i,22j , and V i,u (t, x) (i, j ∈ {1, 2}) to be 2, we can finally obtain the required uncertainty-dependent Lyapunov function V u(⋅) (t, x). Moreover, we can also numerically obtain the required uncertainty-independent piecewise function V(t, x) defined by V 1 (t, x) = (13.747 +…”

Section: F I G U R Ementioning

confidence: 99%

“…Among a great deal of issues on uncertain switched systems, stability problem is an active research field in control theory and engineering 12‐27 . Thus, there have been fruitful results on switched systems with diverse uncertainty such as parametric uncertainty, 13,15,16,22,23 dynamic uncertainty, 14,17,25 interval uncertainty, 12,19,25 polytopic uncertainty, 18‐21,24 structural uncertainty, 26 external disturbance 27 and so on. Among these literatures, numerous excellent sufficient conditions for the stability of different versions of uncertain switched systems were proposed.…”

Section: Introductionmentioning

confidence: 99%

“…Among a great deal of issues on uncertain switched systems, stability problem is an active research field in control theory and engineering. [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] Thus, there have been fruitful results on switched systems with diverse uncertainty such as parametric uncertainty, 13,15,16,22,23 dynamic uncertainty, 14,17,25 interval uncertainty, 12,19,25 polytopic uncertainty, [18][19][20][21]24 structural uncertainty, 26 external disturbance 27 and so on. Among these literatures, numerous excellent sufficient conditions for the stability of different versions of uncertain switched systems were proposed.…”

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Uniform exponential stability criteria with verification for nonautonomous switched nonlinear systems with uncertainty

She

Liu

2022

Intl J Robust & Nonlinear

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This article is concerned with the sufficient and necessary conditions for the global uniform exponential stability (GUES) of a class of uncertain nonautonomous switched nonlinear systems (UNSNS), that is, systems with time-varying uncertain information. To start with, based on a piecewise continuous scalar function and a piecewise differentiable uncertainty-dependent Lyapunov function along the trajectories, we propose alternative sufficient and necessary conditions for the GUES of UNSNS. Afterwards, for removing the dependence on uncertain information of the required Lyapunov functions, we combine an uncertainty-independent Lyapunov function with its right upper Dini derivative and the above piecewise continuous scalar function to further obtain other alternative sufficient and necessary conditions for the GUES of UNSNS. Note that our conditions release the requirement on negative definiteness of the time-derivatives and Dini derivatives of Lyapunov functions respectively, which is illustrated by Example 1. Further, for the rational UNSNS, we propose a linear semidefinite programming based computable approach to mechanically verify our current theoretical results. In the end, the effectiveness of our theoretical results and mechanical approach are illustrated by two examples.

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Input–output finite-time stabilisation for periodic piecewise polynomial systems with nonlinear actuator faults: an observer-based approach

Sakthivel,

Aravinth,

Satheesh

et al. 2023

International Journal of Systems Science

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Stability analysis and robust performance of periodic discrete-time uncertain systems via structured Lyapunov functions

Cited by 4 publications

References 20 publications

Disturbance Observer-Based Robust Control Design for Uncertain Periodic Piecewise Time-Varying Systems With Disturbances

Disturbance Observer-Based Robust Control Design for Uncertain Periodic Piecewise Time-Varying Systems With Disturbances

Uniform exponential stability criteria with verification for nonautonomous switched nonlinear systems with uncertainty

Input–output finite-time stabilisation for periodic piecewise polynomial systems with nonlinear actuator faults: an observer-based approach

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