Linear matrix inequality approach to local stability analysis of discrete‐time Takagi–Sugeno fuzzy systems

Lee, Dong Hwan; Joo, Young Hoon; Tak, Myung Hwan

doi:10.1049/iet-cta.2013.0033

Cited by 23 publications

(16 citation statements)

References 38 publications

(102 reference statements)

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“…More examples with possible MO formulations in the form of (1) are discussed as follows. In [36] and [37], the problem of computing the region of attraction (ROA) was investigated. Suppose that the estimation of the ROA of a system has been formulated as an SOP with LMI constraints and that a robust control law is desired to stabilize the system.…”

Section: Proofmentioning

confidence: 99%

Multiobjective controller design by solving a multiobjective matrix inequality problem

Chiu

2014

IET Control Theory & Applications

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In this study, linear matrix inequality (LMI) approaches and multiobjective (MO) evolutionary algorithms are integrated to design controllers. An MO matrix inequality problem (MOMIP) is first defined.A hybrid MO differential evolution (HMODE) algorithm is then developed to solve the MOMIP. The hybrid algorithm combines deterministic and stochastic searching schemes. In the solving process, the deterministic part aims to exploit the structures of matrix inequalities, and the stochastic part is used to fully explore the decision variable space. Simulation results show that the HMODE algorithm can produce an approximated Pareto front (APF) and Pareto-efficient controllers that stabilize the associated controlled system. In contrast with single-objective designs using LMI approaches, the proposed MO methodology can clearly illustrate how the objectives involved affect each other, i.e., a broad perspective on optimality is provided. This facilitates the selecting process for a representative design, and particularly the design that corresponds to a nondominated vector lying in the knee region of the APF. In addition, controller gains can be readily modified to incorporate the preference or need of a system designer.W.-Y. Chiu is with the Multiobjective Control Lab,

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Section: Proofmentioning

confidence: 99%

Multiobjective controller design by solving a multiobjective matrix inequality problem

Chiu

2014

IET Control Theory & Applications

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“…Research directions to reduce the conservatism include approaches searching for general classes of Lyapunov functions, such as piecewise Lyapunov functions [9,10], fuzzy Lyapunov functions (FLFs) [11][12][13][14][15][16], a class of Lyapunov functions using line-integral [17]; polynomial Lyapunov functions [18][19][20][21]; augmented FLFs [22][23][24]; methods using information on MFs' shape [25][26][27], Pólya's theorem [28][29][30][31][32][33]; and local stability approaches [34][35][36][37][38][39][40][41][42][43][44][45]. Amongst the promising research topics, in this paper, we focus on the local stability approaches, which have turned out to be effective in improving the global approaches further [34][35][36][37][38][39][40][41][42]…”

Section: Introductionmentioning

confidence: 99%

“…Amongst the promising research topics, in this paper, we focus on the local stability approaches, which have turned out to be effective in improving the global approaches further [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51]. Evaluation of the local stability is the problem of determining if there exists a neighborhood of the equilibrium point, called the domain of attraction (DA) [46], such that all trajectories of the system emanating from any initial point in the DA asymptotically converges to the equilibrium point.…”

Section: Introductionmentioning

confidence: 99%

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LMI conditions for local stability and stabilization of continuous-time T-S fuzzy systems

Lee

Joo

Tak

2015

Int. J. Control Autom. Syst.

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In this paper, we propose linear matrix inequality (LMI) formulations to analyze local stability and design controllers that locally stabilize continuous-time nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy systems. In order to estimate the domain of attraction (DA), the so-called fuzzy Lyapunov function is used to characterize the subsets of the DA as sublevel sets of the Lyapunov function. Quadratic bounds on the time-derivative of the membership functions are employed to derive the main results. Finally, examples are given to illustrate the proposed methods.

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“…Nowadays, digital control systems are ubiquitous in real engineering applications, thanks to the rapid advancement of digital computer technology [1,[25][26][27][28][29][30][31][32][33][34][35]. Continuous-time (CT) systems controlled by a digital controller are referred to as sampled-data (SD) control systems, shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

LMI-based robust sampled-data stabilization of polytopic LTI systems: A truncated power series expansion approach

Lee

Joo

2015

Int. J. Control Autom. Syst.

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For continuous-time linear time-invariant (LTI) systems with polytopic uncertainties, we develop a robust sampled-data state-feedback control design scheme in terms of linear matrix inequalities (LMIs). Truncated power series expansions are used to approximate a discretized model of the original continuous-time system. The system matrices obtained by using the power series approximations are then expressed as homogeneous polynomial parameter-dependent (HPPD) matrices of finite degrees, and conditions for designing the controller are formulated as a HPPD matrix inequality, which can be solved by means of a recent LMI relaxation technique to test the positivity of HPPD matrices with variables in the simplex. To take care of the errors induced by the remainder terms of the truncated power series, the terms are considered as norm bounded uncertainties and then incorporated into the proposed LMI conditions. Finally, examples are used to illustrate the approach.

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Linear matrix inequality approach to local stability analysis of discrete‐time Takagi–Sugeno fuzzy systems

Cited by 23 publications

References 38 publications

Multiobjective controller design by solving a multiobjective matrix inequality problem

Multiobjective controller design by solving a multiobjective matrix inequality problem

LMI conditions for local stability and stabilization of continuous-time T-S fuzzy systems

LMI-based robust sampled-data stabilization of polytopic LTI systems: A truncated power series expansion approach

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