In this paper we consider stability analysis and controller design for periodic Takagi-Sugeno fuzzy models. To develop the conditions, we use a switching nonquadratic Lyapunov function defined at the time instants when the subsystems switch. Using the proposed conditions we are able to handle periodic Takagi-Sugeno systems where the local models or even the subsystems are unstable or cannot be ...

Three different types of universal integral based on level dependent capacities are introduced and discussed. Two extremal types are based on Caratheodory’s idea of inner and outer measures, while the third type is introduced for copula-based universal integrals only. Keywords—Choquet integral, Copula, Fuzzy measure, Level dependent capacities, Sugeno integral, Universal integral.

This paper presents an approach to formally model Takagi–Sugeno– Kang (TSK) fuzzy systems without the use of any external components. In order to keep the model continuity, the formal simulation model for a TSK fuzzy system is comprised of three types of reusable sub-models involving primitive operations. Thus, the model can be executed even on limited computational platforms, such as embedded ...

This paper discusses the stabilization of Takagi–Sugeno (T–S) fuzzy systems with bounded and time-varying input delay. The robust stabilization via state feedback is first addressed, and delay-dependent stabilization conditions are proposed in terms of LMIs. Observer-based feedback stabilization is also discussed for T–S fuzzy input delay systems without uncertainties. A separate design princip...

This paper presents the nano-positioning control of a piezoelectric platform. A Bouc-Wen model is established to describe the nonlinear hysteretic effect of piezoelectric systems. Three kinds of compensators, traditional PI controller, PI-like fuzzy logic controller (FLC) and adaptive PI-FLC controller, are designed for the piezoelectric systems. The adaptive PI controller is tuned on-line by m...

Most fuzzy control papers check LMI or SOS stability conditions in order to prove local stability results of nonlinear systems (Takagi-Sugeno fuzzy models or polynomial fuzzy models via Sector Nonlinearity approach). In case of having into account the shape of the membership functions in a particular region of interest, less conservative stability and stabilization conditions can be easily set ...

This paper presents a survey on the ex isting methods for the stability analysis of fuzzy control systems including both conventional Mamdani s rule based fuzzy controllers and Takagi Sugeno controllers The overview considers several approaches including input output stability frequency response methods Lyapunov techniques and qualitative methods The paper also sumarizes the new stability techn...

In this paper, based on the off-axis circle criterion, a sufficient condition with a simple graphical explanation is derived to analyze the global asymptotic stability of a type of Takagi-Sugeno (T-S) fuzzy control systems in case of different constant reference inputs. Three numerical examples are given to demonstrate how to use the proposed method in analyzing the T-S fuzzy control systems.

This paper is concerned with stabilization problem of continuous-time Takagi-Sugeno fuzzy systems. To do this, the stabilization problem is investigated based on the new fuzzy Lyapunov functions (NFLFs). The NFLFs depend on not only the fuzzy weighting functions but also their first-time derivatives. The stabilization conditions are derived in terms of linear matrix inequalities (LMIs) which ca...

This paper examines the inverse control problem of nonlinear systems with stable dynamics using a fuzzy modeling approach. Indeed, based on the ability of fuzzy systems to approximate any nonlinear mapping, the nonlinear system is represented by a Takagi-Sugeno (TS) fuzzy system, which is then inverted for designing a fuzzy controller. As an application of the proposed inverse control methodolo...