Further Study on Observer Design for Continuous-Time Takagi-Sugeno Fuzzy Model with Unknown Premise Variables via Average Dwell Time

This article further studies the problem of observer design for the continuous-time Takagi-Sugeno (T-S) fuzzy system with unmeasurable premise variables. A membership function-dependent Lyapunov function is designed to obtain the observer-based controller. Different from the existing results, a switching method is proposed to deal with the time derivative of membership functions. Several problems such as, too many parameters, and the small local stabilization region in the existing papers are solved by applying the switching method. In addition, two algorithms are designed to obtain the controller gains and observer gains. In the end, two examples are provided to demonstrate the effectiveness of the proposed approach. </p

2-Hydroxy-N,N′-diisopropylpropane-1,3-diaminium dichloride

In the crystal structure of the title amino alcohol derivative, C9H24N2O2+·2Cl−, the cations and anions are linked by inter­molecular O—H⋯Cl and N—H⋯Cl hydrogen bonds into a three-dimensional network

Event-triggered dissipative filtering for stochastic fuzzy complex networks under multiple cyber-attacks

This article investigates the problem of event-based strictly dissipative filtering for stochastic fuzzy complex networks (SFCNs) subject to multiple cyberattacks, including deception attacks and denial-of-service (DoS) attacks. A resilient event-triggered mechanism (ETM) is proposed to reduce the communication burden while effectively countering these cyberattacks. The membership functions are assumed to be mismatched due to the impact of the network environment and sampling behavior. Furthermore, the system dynamics are modeled using Itô-type stochastic differential equations, which include deterministic fuzzy complex networks (CNs) as a special case. Unlike previous studies on stochastic systems, the auxiliary vector function method is employed to introduce more time-varying delay information into the piecewise Lyapunov–Krasovskii functional (LKF), thus reducing conservatism. Consequently, a series of delay-dependent sufficient conditions is derived to ensure the exponentially mean-square stability (EMSS) and strict dissipativity of the filtering error system. Finally, the effectiveness of the proposed method is demonstrated through an illustrative example

Stability and stabilization of positive fuzzy systems via polynomial Lyapunov functions with application to tank level control

In this paper, new stability conditions are obtained by designing a Lyapunov function that contains polynomials of the system states and membership functions. An iterative algorithm is designed to solve the stabilization problem. Since more free variables are introduced by using the square root of the system states and square matrix representation, the proposed conditions are less conservative than existing ones. Furthermore, the time derivative of the membership functions is dealt with by applying polynomial switching mechanism, while the average dwell time approach is employed to address the switching signal. The effectiveness of the proposed method is demonstrated through three numerical examples, including a practical tank level control system, confirming its applicability to real-world scenarios. This paper shows that for positive fuzzy systems, better results can be achieved by utilizing the positivity of the system states and the information of the membership functions. Note to Practitioners—Positive fuzzy systems have found wide applications in engineering domains such as chemical process control, biological systems, and water resource management, where system variables are inherently non-negative. However, traditional control methods often fail to fully exploit the structural characteristics of such systems, resulting in conservative designs and limited performance. Motivated by these challenges, this paper proposes a new stabilization approach that utilizes the positivity of the system states and the information of the membership functions. A Lyapunov function is constructed by incorporating the square roots of state polynomials and polynomial terms of the membership functions, and an iterative algorithm is developed to solve the associated stabilization conditions. Furthermore, the relationship between the stability region and the degree of the polynomials is investigated, which has important implications for enhancing overall system performance

Finite-Time Asynchronous Switching Control for Fuzzy Markov Jump Systems by Applying Polynomial Membership Functions

This article addresses the problem of finite-time asynchronous switching control for fuzzy Markov jump systems (FMJSs) using polynomial membership functions. Firstly, a Lyapunov-Krasovskii functional (LKF) is designed, incorporating both system modes and polynomial membership functions. This LKF contains more information about the membership functions, closely aligning with the characteristics of FMJSs, and effectively reducing conservatism. Based on the polynomial matrices switching rule, a practical asynchronous switching controller is introduced. The objective is to ensure finite-time boundedness of the closed-loop FMJSs while satisfying a H∞ performance index. Furthermore, the average dwell time method is applied to handle the switching signal, eliminating the predefined assumptions that switching numbers are finite or that system states are constrained to a specific region. Ultimately, the validity and practicability of the obtained results are verified through three examples

A switching asynchronous control approach for Takagi-Sugeno fuzzy Markov jump systems with time-varying delay

Till now, most of the results on T-S (Takagi-Sugeno) fuzzy Markov jump systems are synchronous and independent of the analysis of membership functions (MFs), which leads to conservatism. Therefore, it is significant to study the MFs-dependent Lyapunov-Krasovskii functional (LKF) while consid-ering asynchrony. This article investigates the &lt;inline-formula&gt;&lt;tex-math notation="LaTeX"&gt;$H_\infty$&lt;/tex-math&gt;&lt;/inline-formula&gt; control issue of T-S fuzzy Markov jump systems with time-varying delay. First, delay-product-type (DPT) terms and MFs are introduced to design a new LKF, which fully utilizes the information of time-varying delay and MFs simultaneously. Moreover, based on a hidden Markov model, the controller mode is assumed to operate asynchronously with the system mode, and an asynchronous switching fuzzy controller is proposed by employing the switching approach. Thus a more practical and less conservative stability criterion is obtained to ensure the closed-loop system is stochas-tically stable with &lt;inline-formula&gt;&lt;tex-math notation="LaTeX"&gt;$H_\infty$&lt;/tex-math&gt;&lt;/inline-formula&gt; performance. Finally, three examples are provided to illustrate the superiority and practicability of the presented method.</p