Dynamic output-feedback control for singular T–S fuzzy systems using fuzzy Lyapunov functions

Park, In Seok; Kwon, Nam Kyu; Park, PooGyeon

doi:10.1007/s11071-019-05300-2

Cited by 21 publications

(10 citation statements)

References 43 publications

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“…Since the time derivatives, unlike FBFs, cannot belong to a unit simplex, it is quite difficult to exclude them from the stabilization conditions via the convex combination approach. Recently, several attempts to solve this issue have been made on the assumption that the boundary constraints on the time derivatives can be sufficiently tuned through postprocessing based on simulation results (see [19,26,28] and references therein for details). However, for that assumption to always hold, the operating range of T-S fuzzy systems needs to be locally limited.…”

Section: Introductionmentioning

confidence: 99%

Nonquadratic local stabilization of T-S fuzzy systems via improved slack-variable-free relaxation technique under limited operating region

Kim

2022

Preprint

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This paper aims to investigate the problem of nonquadratic local stabilization and disturbance attenuation for Takagi-Sugeno (T-S) fuzzy systems under the limited operating region of premise variables. To derive less conservative local stabilization conditions, this paper first proposes a parameterized linear matrix inequality (PLMI) formulation method that enables both the nonquadratic Lyapunov function and the non-parallel distributed compensation (non-PDC) control scheme. Specifically, in the PLMI formulation, the time derivatives of fuzzy basis functions are addressed without any boundary assumptions and by avoiding excessive use of inequality constraints and slack variables. Moreover, an effective relaxation technique is proposed to obtain a finite set of LMIs from PLMIs in a less conservative way without extra slack variables. Finally, three examples are provided to illustrate the effectiveness of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Nonquadratic local stabilization of T-S fuzzy systems via improved slack-variable-free relaxation technique under limited operating region

Kim

2022

Preprint

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“…In light of such models, a close relationship between the fuzzy logic theory and the sophisticated linear systems theory can be established to realize the control design for nonlinear systems. As a result, a series of topics on T-S fuzzy systems have been well discussed [21][22][23][24][25][26][27][28][29][30]. Although many interesting observer design methods have been explored for T-S fuzzy systems, they are not directly applicable for T-S fuzzy singular systems (TSFSSs).…”

Section: Introductionmentioning

confidence: 99%

Robust observer design for T-S fuzzy singular systems with unmeasurable premise variables and partially decoupled disturbances

Cai

et al. 2022

Preprint

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This article makes some efforts towards discussing the problem of observer design for a kind of discrete-time T-S fuzzy singular systems corrupted by process disturbances and measurement noises. To situate our design scheme in a more practical context, the premise variables of fuzzy systems under consideration are unmeasurable, and the process disturbances are only partially decoupled rather than completely decoupled. By integrating the fuzzy Lyapunov function method and the linear matrix inequality technique, an unknown input observer which can not only decouple partial process disturbances, but also attenuate the influence of measurement noises and non-decoupled process disturbances is proposed to achieve state reconstruction. Particularly, to reduce the conservatism, some slack matrices and scalars are utilized in observer design to obtain extra degrees of freedom. Finally, the performance of theoretical results is fully verified via two numerical simulations.

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“…Any controlling law designed based on a linearized representation is a compromise [13]. For this reason, state-of-the-art methods have been introduced to hydroelectric systems, for instance, sliding mode control [14][15][16][17], fuzzy control [18,19], predictive control [20,21], and so on.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear finite‐time control of hydroelectric systems via a novel sliding mode method

Zhang

Ren

Mahmud

et al. 2022

IET Generation Trans & Dist

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A nonlinear finite-time sliding mode control is proposed in this paper for the governing of complex hydroelectric systems with the finite/fixed setting time. The proposed control method is derived from the finite-time stability and sliding mode control theories. The finite settling time is calculated and bounded, not depending on the initial conditions of the system. The solution trajectory of the controlled hydroelectric system can reach the sliding manifold in a fixed settling time, regardless of initial values. Based on the Lyapunov theory, the controlled hydroelectric system also converges to a reference state within the fixed settling time. A simulation of a high-dimensional hydroelectric system verifies the feasibility of the proposed method. In addition, a comparison between the proposed method and the conventional PID method demonstrates the advantages of the proposed method in the shorter settling time and smaller overshoot. The proposed control method allows for the design of a flexible controller and provides an improvement in dynamic performance.

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Dynamic output-feedback control for singular T–S fuzzy systems using fuzzy Lyapunov functions

Cited by 21 publications

References 43 publications

Nonquadratic local stabilization of T-S fuzzy systems via improved slack-variable-free relaxation technique under limited operating region

Nonquadratic local stabilization of T-S fuzzy systems via improved slack-variable-free relaxation technique under limited operating region

Robust observer design for T-S fuzzy singular systems with unmeasurable premise variables and partially decoupled disturbances

Nonlinear finite‐time control of hydroelectric systems via a novel sliding mode method

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