H∞ Static Output-Feedback Gain-Scheduled Control for Discrete LPV Time-Delay Systems

Rosa, Tábitha E.; Frezzatto, Luciano; Morais, Cecília F.; Oliveira, Ricardo C. L. F.

doi:10.1016/j.ifacol.2018.11.155

Cited by 7 publications

(6 citation statements)

References 23 publications

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“…, and (15) with k ∈ Ξ and ij satisfying ij = 1 if i ≠ j, and ij = 0 otherwise. Therefore, the closed-loop system can be described as:…”

Section: Augmented Delay-free Systemmentioning

confidence: 99%

“…11 In this context, various methods to analyze the stability and to design parameter varying dynamic feedback controllers have been proposed for LPV continuous-time systems 12,13 and for the discrete-time counterparts. 14,15 It is worth to say that discrete-time models, which are the focus of this work, have an attractive issue because of their use to design and to implement digital controllers. 16,17 Another practical issue concerns the physical and safety limitations imposed by actuators, which can also lead the closed-loop system to degenerate performance and even to lose stability at some operational conditions.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, LPV systems affected by delays have attracted the attention of researchers in the last few years, because of both the possible performance degradation and the loss of stability induced by the presence of the delay 11 . In this context, various methods to analyze the stability and to design parameter varying dynamic feedback controllers have been proposed for LPV continuous‐time systems 12,13 and for the discrete‐time counterparts 14,15 . It is worth to say that discrete‐time models, which are the focus of this work, have an attractive issue because of their use to design and to implement digital controllers 16,17 …”

Section: Introductionmentioning

confidence: 99%

“…and the system data given in the Example 1 we get the matrices 11  12  21  22  11  12  21  22that replaced in(14) yields A c ( k , k ), B c0 ( k ), and B c1 ( k ), and that replaced in(15) yields C c ( k ), D c0 ( k ), D c1 ( k ), and E c ( k ).…”

mentioning

confidence: 99%

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Dynamic controllers for local input‐to‐state stabilization of discrete‐time linear parameter‐varying systems with delay and saturating actuators

Souza¹,

Castelan²,

Leite

2020

Intl J Robust & Nonlinear

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We address the design of dynamic parameter-dependent controllers with antiwindup action to locally stabilize in the input-to-state sense a class of discrete-time linear parameter-varying (LPV) systems. Such a class consists of systems with delayed state, saturating actuators, and subject to energy bounded disturbances. Moreover, the interval time-varying delay can have a limited variation rate between two consecutive instants allowing to achieve less conservative design conditions. Differently from other conditions in the literature, the proposed convex synthesis methods allow to design dynamic controllers of different orders. Additionally, the user can choose to feed back only the current output of the system or its delayed ones. Thanks to the embedded (parameter dependent) antiwindup action, it is possible, for instance, to enlarge the region of admissible initial conditions or the maximum admissible disturbance energy. To illustrate the efficiency of our approach, we present numerical examples to compare with other methods from the literature. K E Y W O R D S 2-disturbances, dynamic controller, local input-to-state stability, LPV discrete-time systems, saturating actuators, time-varying delay with bounded variation rate Abbreviations: LMI, linear matrix inequality; LPV, linear parameter-varying.

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“…, and (15) with k ∈ Ξ and ij satisfying ij = 1 if i ≠ j, and ij = 0 otherwise. Therefore, the closed-loop system can be described as:…”

Section: Augmented Delay-free Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Dynamic controllers for local input‐to‐state stabilization of discrete‐time linear parameter‐varying systems with delay and saturating actuators

Souza¹,

Castelan²,

Leite

2020

Intl J Robust & Nonlinear

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“…A gain‐scheduled static state‐feedback controller is then designed to meet the performance requirements. In another work, a robust static gain‐scheduled controller design for discrete‐time polytopic LPV systems with a state delay has been formulated in a delay‐independent matrix inequality framework [30]. Dilated delay‐dependent linear matrix inequalities (LMIs) for the control of state‐delay polytopic LPV systems have been addressed in [31].…”

Section: Introductionmentioning

confidence: 99%

Robust delay‐dependent LPV synthesis for blood pressure control with real‐time Bayesian parameter estimation

Tasoujian

Salavati

Franchek

et al. 2020

IET Control Theory & Appl

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Mean arterial blood pressure (MAP) dynamics estimation and its automated regulation could benefit the clinical and emergency resuscitation of critical patients. In order to address the variability and complexity of the MAP response of a patient to vasoactive drug infusion, a parameter-varying model with a varying time delay is considered to describe the MAP dynamics in response to drugs. The estimation of the varying parameters and the delay is performed via a Bayesian-based multiple-model square root cubature Kalman filtering approach. The estimation results validate the effectiveness of the proposed random-walk dynamics identification method using collected animal experiment data. Following the estimation algorithm, an automated drug delivery scheme to regulate the MAP response of the patient is carried out via time-delay linear parameter-varying (LPV) control techniques. In this regard, an LPV gain-scheduled output-feedback controller is designed to meet the MAP response requirements of tracking a desired reference MAP target and guarantee robustness against norm-bounded uncertainties and disturbances. In this context, parameter-dependent Lyapunov-Krasovskii functionals are used to derive sufficient conditions for the robust stabilization of a general LPV system with an arbitrarily varying time delay and the results are provided in a convex linear matrix inequality (LMI) constraint framework. Finally, to evaluate the performance of the proposed MAP regulation approach, closed-loop simulations are conducted and the results confirm the effectiveness of the proposed control method against various simulated clinical scenarios.

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Stabilization and disturbance rejection with decay rate bounding in discrete‐time linear parameter‐varying systems via ℋ_∞gain‐scheduling static output feedback control

Sereni

Assunção

Teixeira

2022

Intl J Robust & Nonlinear

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The stabilization of discrete‐time linear parameter‐varying (LPV) systems via gain‐scheduling static output feedback (SOF) control is addressed in this article. We propose new sufficient linear matrix inequalities (LMI) conditions for synthesizing a gain‐scheduled SOF controller that ensures asymptotic stability and also imposes a lower bound on the closed‐loop decay rate. The SOF controller design is based on a two‐step method: a state‐feedback controller is obtained in a first‐stage design, which is then used as input information in the second stage for computing the desired gain‐scheduled SOF controller. The proposed LMI constraints are given in terms of the existence of affine parameter‐dependent Lyapunov functions, considering arbitrarily fast variation of the time‐varying parameters. An extension for coping with disturbance rejection is also proposed, in terms of the scriptH∞$$ {\mathcal{H}}_{\infty } $$ guaranteed cost optimization. Some numerical experiments are presented to illustrate the control synthesis procedure and its efficacy. Also, feasibility analyses are presented to compare and show the advantages of our results over other available strategies present in literature.

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H∞ Static Output-Feedback Gain-Scheduled Control for Discrete LPV Time-Delay Systems

Cited by 7 publications

References 23 publications

Dynamic controllers for local input‐to‐state stabilization of discrete‐time linear parameter‐varying systems with delay and saturating actuators

Dynamic controllers for local input‐to‐state stabilization of discrete‐time linear parameter‐varying systems with delay and saturating actuators

Robust delay‐dependent LPV synthesis for blood pressure control with real‐time Bayesian parameter estimation

Stabilization and disturbance rejection with decay rate bounding in discrete‐time linear parameter‐varying systems via ℋ_∞gain‐scheduling static output feedback control

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H∞ Static Output-Feedback Gain-Scheduled Control for Discrete LPV Time-Delay Systems

Cited by 7 publications

References 23 publications

Dynamic controllers for local input‐to‐state stabilization of discrete‐time linear parameter‐varying systems with delay and saturating actuators

Dynamic controllers for local input‐to‐state stabilization of discrete‐time linear parameter‐varying systems with delay and saturating actuators

Robust delay‐dependent LPV synthesis for blood pressure control with real‐time Bayesian parameter estimation

Stabilization and disturbance rejection with decay rate bounding in discrete‐time linear parameter‐varying systems via ℋ∞gain‐scheduling static output feedback control

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Stabilization and disturbance rejection with decay rate bounding in discrete‐time linear parameter‐varying systems via ℋ_∞gain‐scheduling static output feedback control