Stabilization of Positive Systems With Time Delay via the Takagi–Sugeno Fuzzy Impulsive Control

Abstract

In this study, the Takagi-Sugeno (T-S) fuzzy impulsive control problem is investigated for a class of nonlinear positive systems with time delay. The time delay under consideration is both in the continuous-time dynamics and at the impulsive instants, which can model practical systems more accurately. An impulse-time-dependent copositive Lyapunov function (IDCLF) is constructed, and the Razumikhin technique is adopted to develop conditions that ensure the globally exponential stability of T-S fuzzy positive systems with delayed impulses. The size constraint between the impulse delay and the bound of impulsive intervals is removed. A T-S fuzzy impulsive controller is designed in terms of the solutions to certain vector inequalities that are readily solvable. Numerical examples and a practical example of lipoprotein metabolism and potassium ion transfer model are given to demonstrate the effectiveness, advantages, and practicality of the proposed results.

Impulsive control of unstable homogeneous positive systems of degree one with unbounded time‐varying delay

“…Remark It is worth pointing out that the stability of Example 1 cannot be studied by the results in Hu et al, 30 Yang and Zhang, 31 Zhu et al, 34 and Hu et al, 35 since the time delay in Example 1 is unbounded and time‐varying.…”

“…Yang and Zhang 33 further analyzed the problems of finite‐time stability and stabilization of homogeneous impulsive positive systems of degree one. The problems of robust stability and stabilization of uncertain impulsive positive delay systems were studied by Zhu et al 34 The Takagi‐Sugeno fuzzy impulsive control problem of positive delay systems was considered in the work of Hu et al 35 It is worth noting that those results in Hu et al, 30 Yang and Zhang, 31 Zhu et al, 34 and Hu et al 35 mainly focus on the impulsive control of positive systems with bounded delays. There are almost no results for impulsive control of positive systems with unbound delays, as the model depends on the whole past information, moreover, the discrete and discontinuous feature of impulses complicate the structure 26,36 .…”

Exponential stability and stabilization of positive T‐S fuzzy delayed systems

“…In Reference 4, an asymptotic stabilization of delayed positive coupled differential equations is assessed. In a recent paper, 17 the authors have studied the stabilization problem for nonlinear delayed positive systems. The proposed independent delay conditions and a single integral‐term based Lyapunov function has been considered for the stability synthesis.…”

“…Compared to Reference 20, the proposed stability conditions in this paper are designed for nonlinear systems without any transformation. To reduce the conservatism, delay‐dependent conditions are established using double‐integral terms based on Lyapunov–Krasovskii functional (differently from Reference 17, where single‐integral terms are considered). The paper's proposed results are formulated in terms of LMI without considering neither parametrization nor CCL algorithm.…”

Fuzzy-Model-Based Control for Markov Switching Singularly Perturbed Systems with the Stochastic Communication Protocol

“…Compared with the standard MSSs, the Markov switching nonlinear systems are more general as they contain high nonlinearity. Lately, the T-S fuzzy model has been tendered to deal with the system's nonlinearities [9,10]. Benefit from the T-S fuzzy model, many Markov switching nonlinear systems can be approximated as T-S fuzzy MSSs (FMSSs).…”