Further results on robust fuzzy dynamic systems with LMI D-stability constraints

Abstract

This paper examines the problem of designing a robust H∞ fuzzy controller with D-stability constraints for a class of nonlinear dynamic systems which is described by a Takagi-Sugeno (TS) fuzzy model. Fuzzy modelling is a multi-model approach in which simple sub-models are combined to determine the global behavior of the system. Based on a linear matrix inequality (LMI) approach, we develop a robust H∞ fuzzy controller that guarantees (i) the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value, and (ii) the closed-loop poles of each local system to be within a specified stability region. Sufficient conditions for the controller are given in terms of LMIs. Finally, to show the effectiveness of the designed approach, an example is provided to illustrate the use of the proposed methodology.

LMI conditions for non-quadratic stabilization of T-S models with pole placement assignation

“…Let us now consider an arbitrary scalar ε, one may introduce the null terms: (29) with (30) and (31), it yields:…”

“…Indeed, ensuring the asymptotic stability does not necessarily mean ensuring a good transient response of the closed-loop system. In this context, some interesting works were carried out in order to improve the closed-loop transient response by adding pole placement constraints to the stabilization problem [28], [29], [30], [31]. Nevertheless, these results are given in the quadratic framework (or piecewise quadratic), which suffer from the above discussed concerns.…”

Modified T2FSMC approach for solar panel systems

“…Harrabi, Kharrat, Aitouche, and Souissi (2018) have applied a fuzzy approach to wind generation systems. Assawinchaichote (2014) has combined fuzzy and H ∞ for a class of nonlinear systems.…”

Dissipative Analysis and Synthesis of Control for TS Fuzzy Markovian Jump Neutral Systems

“…The Takagi-Sugeno (TS) fuzzy model is an effective one to analyze and synthesize nonlinear systems which are ubiquitous in signal processing, communications, chemical processes, robotics systems, and automotive systems [1][2][3]. In recent years, fuzzy control systems have become an important topic in systems theory due to their potential applications in many fields of science and engineering [4,5]. More precisely, Takagi-Sugeno (TS) fuzzy model based control plays an important role which offers a systematic and effective platform for control of nonlinear plants [6,7].…”