Robust Stabilization for Uncertain Takagi-Sugeno Fuzzy Continuous Model with Time-Delay Based on Razumikhin Theorem

New sufficient conditions for delay-independent and delay-dependent robust stability of uncertain fuzzy time-delay systems based on uncertain fuzzy Takagi-Sugeno (T-S) models are presented by using the properties of matrix and norm measurements. Further sufficient conditions are formulated, in terms of the linear matrix inequalities (LMIs) of robust stabilization, and are developed via the technique of parallel distributed compensation (PDC), and then the simplification of the conditions for the controller design of uncertain fuzzy time-delay systems. The proposed methods are simple and effective. Some examples below are presented to illustrate our results.

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Robust Stabilization of Interval Plants with Uncertain Time-Delay Using the Value Set Concept

Mathematics ◽

10.3390/math9040429 ◽

2021 ◽

Vol 9 (4) ◽

pp. 429

Author(s):

Pedro Zamora ◽

Alejandro Arceo ◽

Noé Martínez ◽

Gerardo Romero ◽

Luis E. Garza

Keyword(s):

Time Delay ◽

Robust Stabilization ◽

Parametric Uncertainty ◽

Exclusion Principle ◽

Control Synthesis ◽

Classical Orthogonal Polynomials ◽

Loop Control ◽

Value Set ◽

Interval Plants ◽

Uncertain Time

This paper considers the robust stabilization problem for interval plants with parametric uncertainty and uncertain time-delay based on the value set characterization of closed-loop control systems and the zero exclusion principle. Using Kharitonov’s polynomials, it is possible to establish a sufficient condition to guarantee the robust stability property. This condition allows us to solve the control synthesis problem using conditions similar to those established in the loopshaping technique and to parameterize the controllers using stable polynomials constructed from classical orthogonal polynomials.

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Spatiotemporal Patterns Formed by a Discrete Nutrient-Phytoplankton Model with Time Delay

Complexity ◽

10.1155/2020/8541432 ◽

2020 ◽

Vol 2020 ◽

pp. 1-18

Author(s):

Feifan Zhang ◽

Wenjiao Zhou ◽

Lei Yao ◽

Xuanwen Wu ◽

Huayong Zhang

Keyword(s):

Steady State ◽

Time Delay ◽

Numerical Simulations ◽

Functional Response ◽

Bifurcation Analysis ◽

Discrete Model ◽

Continuous Model ◽

Spatiotemporal Patterns ◽

Homogeneous Steady State ◽

Simulation Results

In this research, a continuous nutrient-phytoplankton model with time delay and Michaelis–Menten functional response is discretized to a spatiotemporal discrete model. Around the homogeneous steady state of the discrete model, Neimark–Sacker bifurcation and Turing bifurcation analysis are investigated. Based on the bifurcation analysis, numerical simulations are carried out on the formation of spatiotemporal patterns. Simulation results show that the diffusion of phytoplankton and nutrients can induce the formation of Turing-like patterns, while time delay can also induce the formation of cloud-like pattern by Neimark–Sacker bifurcation. Compared with the results generated by the continuous model, more types of patterns are obtained and are compared with real observed patterns.

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