On discrete‐time LPV control using delayed Lyapunov functions

Peixoto, Márcia L. C.; Lacerda, Márcio J.; Palhares, Reinaldo M.

doi:10.1002/asjc.2362

Cited by 14 publications

(11 citation statements)

References 35 publications

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“…Moreover, the method in Reference 17 provides gain‐scheduling controllers that are rational in the time‐varying parameters, which are more general than LPV ones. It is also worth mentioning recent results for stability and stabilizability of LPV discrete‐time systems by using nonmonotonic Lyapunov functions 19 and delayed Lyapunov functions 20 . These results have employed LPV input matrices; however, there are no constraints on the input signal.…”

Section: Introductionmentioning

confidence: 99%

Design of saturating state feedback control laws for discrete‐time linear parameter varying systems through homogeneous polynomial parameter‐dependent functions

Figueiredo

Lacerda

Leite

2021

Intl J Robust & Nonlinear

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This article investigates the local stabilization problem for the class of discrete‐time linear parameter varying (LPV) systems subject to saturating actuators. The main contributions are new convex conditions for synthesizing rational parameter‐dependent state feedback gain controllers, ensuring the local stability of the closed‐loop system for a set of initial conditions. We propose two design conditions for the local stabilization of the considered class of systems, which may lead to complementary results. We use a homogeneous polynomial parameter‐dependent (HPPD) based structure on the matrices variables. Thanks to a level set defined from an HPPD based Lyapunov function, we get less conservative estimates of the region of attraction. We provide a generalization of previous formulations from the literature to compute the intersection of parameter‐dependent ellipsoidal sets through finite‐dimensional conditions. The parameter‐dependent controller gains may assume rational structures on the time‐varying parameters, yielding better estimates of the region of attraction, as well as a broad set of stabilizable systems. Two examples illustrate the numerical aspects of the proposed conditions and give the reader a perspective of the relations concerning the conservatism and the degree of the HPPD functions.

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Section: Introductionmentioning

confidence: 99%

Design of saturating state feedback control laws for discrete‐time linear parameter varying systems through homogeneous polynomial parameter‐dependent functions

Figueiredo

Lacerda

Leite

2021

Intl J Robust & Nonlinear

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“…Numerous real-life phenomena can be modeled using LPV systems that involve nonlinearities and uncertainties, [9][10][11]. However, it is worth mentioning that various issues pertaining to LPV framework still remain open with regard to stability analysis and synthesizing control law [12].…”

Section: Introductionmentioning

confidence: 99%

A deterministic approach for design of supervisory control of LPV systems with delay

et al. 2021

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Linear Parameter Varying (LPV) systems and their control have gained attraction recently as they approximate nonlinear systems with higher order than ordinary linear systems. On the other hand, time delay is an inherent part of various real-life applications. A supervisory control structure is proposed in this paper for LPV systems subject to time delays. In the proposed control structure, a supervisor selects the most suitable controller from a bank of controllers; which desires to enhance the performance of closed-loop system in contrast with using a single robust controller. The analysis is based on the celebrated Smith predictor for time delay compensation and we provide a sufficient condition to assure the stability of the closed-loop switched system in terms of dwell time. Simulations on blood pressure control of hypertension patients in postoperative scenario are used to exemplify the effectiveness of the utilized technique. The operating region of the system is partitioned into five smaller operating regions to construct corresponding robust controllers and perform hysteresis switching amongst them. Simulation results witnessed that the proposed control scheme demonstrated a pressure undershoot less than the desired value of 10 mmHg while the Mean Arterial Pressure (MAP) remains within ±5 mmHg of the desired value.

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“…24 In this case, by following the sector nonlinearity approach, 24,25 nonlinear systems are generally rewritten as equivalent local polytopic differential inclusions by subsuming their bounded nonlinear expressions into parameters that compose the polytopic model and are also employed to construct the gain-scheduling control law. Then, mimicking developments for linear parameter-varying systems, [26][27][28] a variety of gain-scheduled controllers can be synthesized with different degrees of conservativeness. [29][30][31] Efforts to cast the problem of stabilization of nonlinear systems via sampled-data controllers as a set of LMI conditions have been made in the past for Lur'e-type systems.…”

Section: Introductionmentioning

confidence: 99%

Robust sampled‐data controller design for uncertain nonlinear systems via Euler discretization

Coutinho

Bernal

Palhares

2020

Intl J Robust & Nonlinear

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Robust stabilization of a class of uncertain nonlinear systems through a sampled-data control law is considered in this work. Based on the forward discrete-time Euler approximation, conditions in the form of linear matrix inequalities are provided to synthesize a discrete controller that guarantees the states to be asymptotically driven to the origin, regardless of the presence of bounded parametric uncertainties. In contrast with other approaches, the system is not required to be Lure-type nor the conditions to have predefined gains to be tested. Examples are given to illustrate the effectiveness of the proposal.

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On discrete‐time LPV control using delayed Lyapunov functions

Cited by 14 publications

References 35 publications

Design of saturating state feedback control laws for discrete‐time linear parameter varying systems through homogeneous polynomial parameter‐dependent functions

Design of saturating state feedback control laws for discrete‐time linear parameter varying systems through homogeneous polynomial parameter‐dependent functions

A deterministic approach for design of supervisory control of LPV systems with delay

Robust sampled‐data controller design for uncertain nonlinear systems via Euler discretization

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