Ho Jae Lee

Fuzzy Stabilization of Nonlinear Systems under Sampled-Data Feedback: An Exact Discrete-Time Model Approach

This paper addresses stabilization problems for a nonlinear system via a sampled-data fuzzy controller. The nonlinear system is assumed to be exactly modeled in Takagi-Sugenos form, at least locally. Unlike the conventional direct discrete-time design approach based on an approximate discrete-time model, the sampled-data fuzzy controllers are designed based on an exact discrete-time model. Sufficient design conditions are formulated in terms of linear matrix inequalities. It is shown that whenever the exact discrete-time fuzzy model is asymptotically stabilizable via the sampled-data fuzzy controller uniformly bounded in the state, then so is the original nonlinear system. A numerical example is given to illustrate the effectiveness of the proposed methodology.

Sampled-data observer-based output-feedback fuzzy stabilization of nonlinear systems: Exact discrete-time design approach

This paper presents a new direct discrete-time design methodology of a sampled-data observer-based output-feedback fuzzy controller for a class of nonlinear system that is exactly modeled in Takagi-Sugenos form at least locally. A fundamental yet challenging issue in this direction is the unavailability of the exact discrete-time model of the nonlinear plant in a closed form. In contrast to the earlier works that are based on an approximate discrete-time model thus the stability obtained in the design step is not preserved in the implementation step, we employ an exact discrete-time fuzzy model in an integral form. Sufficient asymptotic stabilization conditions are investigated in the discrete-time Lyapunov sense. We then show that the resulting sampled-data controller indeed asymptotically stabilizes the nonlinear plant. An example is provided to illustrate the effectiveness of the proposed methodology.

Brief paper: Stability connection between sampled-data fuzzy control systems with quantization and their approximate discrete-time model

This paper concerns the stability of a sampled-data Takagi-Sugeno (T-S) fuzzy control system with quantization, when a controller design is based on an approximate discrete-time model of the plant without quantization. The motivations come from the facts that digital devices for interfacing a plant with a controller quantize signals and an exact discrete-time model of the T-S fuzzy system is generally not amenable to synthesis process. We show that the concerned system is Lagrange stabilizable by the controller asymptotically stabilizing the approximate discrete-time model. A constructive design algorithm for the developed stability analysis is proposed in terms of linear matrix inequalities.

Intelligent digital redesign revisited: Approximate discretization and stability limitation

This paper sharpens the recently developed intelligent digital redesign (IDR) technique in regard of stability. A major assumption in the previous result was that the firing strength of each fuzzy rule is approximated as its sampled value during a sampling period for efficient discretization of the Takagi-Sugeno (T-S) fuzzy system, by which some unexpected stability might be experienced for certain sampling period as large as the assumption is unrealistic. To clarify results for that case, we refine the IDR condition and prove that the uniformly semiglobal practical asymptotic stability of the sampled-data T-S fuzzy control system by the intelligently redesigned digital fuzzy controller, rather than the global exponential stability shown in the previous result.

Comments on "T - S Fuzzy-Model-Based Robust

This letter addresses that the linear matrix inequality condition relaxation for stability of the Takagi-Sugeno fuzzy networked control system is incorrect.

H_{\infty }

Takagi-Sugeno (T--S) fuzzy-model-based static output-feedback controller design is a challenging issue due to the nonconvexity in the Lyapunov stability condition. Recently, a convexified linear matrix inequality (LMI) condition was proposed for the problem by additionally importing as many equality constraints as the number of the fuzzy rules with a variable in the paper from the study of Fang et al. However, numerical experiences seem to imply the infeasibility of the proposed LMI. This letter shows that their LMI problem may be feasible.

Design for Networked Control Systems With Uncertainties

This article develops a digital redesign (DR) technique for sampled-data observer-based output-feedback control of a continuous-time linear system with nonlinear perturbation. It is assumed that the nonlinear perturbation is a locally Lipschitz function. To deal with the discrete-time modelling error in nonlinear systems, as opposed to the previous approach, the DR problem is configured as a stabilisation one for error dynamics between the closed-loop system of nominal linear model under an analogue state-feedback controller and that of the linear system with the nonlinear perturbation under a sampled-data output-feedback controller. A constructive DR condition is formulated in the format of linear matrix inequalities. The stability of the actual sampled-data control system is guaranteed within the DR procedure. The effectiveness of the proposed DR methodology is demonstrated through a numerical simulation.

Fuzzy Static Output Feedback May Be Possible in LMI Framework

This paper presents an efficient design methodology for pulse-width-modulated (PWM) feedback control of a nonlinear system. To avoid the non-causality between the PWM controller and the widely used modulation law – the principle of equivalent area, the analogue controller to be modulated is first digitally redesigned based on the optimal linear model of the nonlinear system, and is then PWM redesigned, which is an extension of our previous result. It is shown that the proposed technique achieves a uniformly semi-globally practically asymptotic stability of the actual nonlinear PWM feedback control system. An example is provided to illustrate the effectiveness of the proposed methodology.

Controlling linear systems with nonlinear perturbations under sampled-data output feedback: digital redesign approach

Digital redesign for observer-based output-feedback tracking controller with time-varying references is developed. The improvements have been done by more precisely approximating the reference and considering the state matching of the estimation error in a plant dynamics for a large sampling period, and by using the delta-operated discrete-time modelling for an extremely small sampling period.