A new discrete-time stabilizability condition for Linear Parameter-Varying systems

Pandey, Amit; Oliveira, Maurı́cio C. de

doi:10.1016/j.automatica.2017.02.006

Cited by 25 publications

(22 citation statements)

References 7 publications

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“…The technique proposed in this article (A1) with

i t_{\max} = 10

is compared with: [44, theorem 2] (PdO); [37, eq. (49)] (dCC) by eliminating the last column and row and considering b = 1 (arbitrarily fast rates of variation); [18, theorem 1] with

γ = - 1 0^{5}

ξ = {- 0.2, - 0.1, 0, 0.1, 0.2}

(RT); [18, algorithm 1] with

ρ = {1.05, 1.1}

and degP=1 (RC) [45, theorem 1] (PCP) with

η \in {1 0^{- 6}, 1 0^{- 5}, \dots, 1, 10, \dots, 1 0^{5}, 1 0^{6}}

(13 values),

X (α_{k}, α_{k + 1})

with multiaffine dependence on

α_{k}

and

α_{k + 1}

, and all the other optimization variables with affine dependence on

α_{k}

. …”

Section: Numerical Examplesmentioning

confidence: 99%

Linear matrix inequality‐based solution for memory static output‐feedback control of discrete‐time linear systems affected by time‐varying parameters

Palma

Morais

Oliveira

2021

Intl J Robust & Nonlinear

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This article investigates the problem of designing static output‐feedback controllers for linear parameter‐varying (LPV) discrete‐time systems through the enrichment of the system dynamics. For this purpose, the past values of the measured outputs are included in the control law. Differently from the previous methods from the literature addressing memory control, a locally convergent iterative procedure based on linear matrix inequalities is proposed to solve the problem. As the main novelty, the procedure deals with the control gains as optimization variables of the problem (no change of variables is necessary), addressing state‐ and output‐feedback in the same way, and allowing to cope with magnitude or structural constraints (such as decentralization) without introducing extra conservativeness. Numerical examples illustrate the effectiveness of the method, providing in general less conservative stabilization results than the existing methods when dealing with LPV systems.

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“…The technique proposed in this article (A1) with

i t_{\max} = 10

is compared with: [44, theorem 2] (PdO); [37, eq. (49)] (dCC) by eliminating the last column and row and considering b = 1 (arbitrarily fast rates of variation); [18, theorem 1] with

γ = - 1 0^{5}

ξ = {- 0.2, - 0.1, 0, 0.1, 0.2}

(RT); [18, algorithm 1] with

ρ = {1.05, 1.1}

and degP=1 (RC) [45, theorem 1] (PCP) with

η \in {1 0^{- 6}, 1 0^{- 5}, \dots, 1, 10, \dots, 1 0^{5}, 1 0^{6}}

(13 values),

X (α_{k}, α_{k + 1})

with multiaffine dependence on

α_{k}

and

α_{k + 1}

, and all the other optimization variables with affine dependence on

α_{k}

. …”

Section: Numerical Examplesmentioning

confidence: 99%

Linear matrix inequality‐based solution for memory static output‐feedback control of discrete‐time linear systems affected by time‐varying parameters

Palma

Morais

Oliveira

2021

Intl J Robust & Nonlinear

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show abstract

“…In order to achieve a less conservative solution, the parameter-dependent matrix P (ρ) is designed in [25,26].…”

Section: Extended Bounded Real Lemmamentioning

confidence: 99%

LPV Model Based Sensor Fault Diagnosis and Isolation for Permanent Magnet Synchronous Generator in Wind Energy Conversion Systems

et al. 2018

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This paper deals with the current sensor fault diagnosis and isolation (FDI) problem for a permanent magnet synchronous generator (PMSG) based wind system. An observer based scheme is presented to detect and isolate both additive and multiplicative faults in current sensors, under varying torque and speed. This scheme includes a robust residual generator and a fault estimation based isolator. First, the PMSG system model is reformulated as a linear parameter varying (LPV) model by incorporating the electromechanical dynamics into the current dynamics. Then, polytopic decomposition is introduced for H ∞ design of an LPV residual generator and fault estimator in the form of linear matrix inequalities (LMIs). The proposed gain-scheduled FDI is capable of online monitoring three-phase currents and isolating multiple sensor faults by comparing the diagnosis variables with the predefined thresholds. Finally, a MATLAB/SIMULINK model of wind conversion system is established to illustrate FDI performance of the proposed method. The results show that multiple sensor faults are isolated simultaneously with varying input torque and mechanical power.

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“…15,18 Adopting = 1, the time-varying parameters vary arbitrarily from the instant k to the instant k + 1 inside Ω N . In this case, other works 19,20,32 have been widely used for analysis and design of controllers. In real-world applications, the time-varying parameters are subject to bounds on their rate of variation and such information are not employed in those references.…”

Section: Preliminariesmentioning

confidence: 99%

Optimal guaranteed cost control for discrete‐time LPV systems with bounded rates of variation

Pereira

Kienitz

Leandro

2018

Optim Control Appl Methods

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In this paper, an optimal guaranteed cost control strategy to stabilize discrete-time linear parameter-varying systems with bounded rates of variation is presented. Sufficient conditions for the synthesis of fixed gain and gain-scheduled guaranteed cost controllers are given in terms of two sets of linear matrix inequalities. The main advantage of the proposed conditions is to rely on the use of homogeneous polynomial parameter-dependent Lyapunov functions of arbitrary degree that allow to assess the stability of the closed-loop system under the prescribed bound on the rate of parameter variations. In order to make the approach feasible, linear matrix inequality relaxations based on Pólya's theorem are addressed. Finally, the effectiveness of the proposed design methods is illustrated through numerical examples.

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A new discrete-time stabilizability condition for Linear Parameter-Varying systems

Cited by 25 publications

References 7 publications

Linear matrix inequality‐based solution for memory static output‐feedback control of discrete‐time linear systems affected by time‐varying parameters

Linear matrix inequality‐based solution for memory static output‐feedback control of discrete‐time linear systems affected by time‐varying parameters

LPV Model Based Sensor Fault Diagnosis and Isolation for Permanent Magnet Synchronous Generator in Wind Energy Conversion Systems

Optimal guaranteed cost control for discrete‐time LPV systems with bounded rates of variation

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