Finite‐time control via hybrid state feedback for uncertain positive systems with impulses

Abstract

In this study, the finite‐time ℒ1 control for uncertain positive systems with impulses using a hybrid state feedback control mechanism is investigated. The hybrid state feedback double control strategy is utilized, which includes impulsive state control scheme and continuous state feedback control scheme. A type of time‐varying Lyapunov copositive function is constructed. Considering different impulsive effects, the finite‐time boundedness criterion is obtained by applying the average impulsive interval approach. In addition, sufficient conditions are proposed for finite‐time ℒ1 characterization analysis and the hybrid state feedback controller design. All the criteria can be checked by the linear programming approach succinctly. The relationships among the upper bound of the finite‐time interval, the frequency and intensity of impulses, and the minimum allowable ℒ1‐gain level are revealed. Numerical examples are used to illustrate the usefulness of the theoretical results.

Finite time stability analysis for T-S fuzzy positive systems and its application in pest control

“…FTS can well reflect the transient performance, so FTS has important research significance in missile system, robot operating system and other systems with short working time. For positive systems, some meaningful results on FTS have been reported [8][9].…”

“…Inspired by the above discussion, this paper studies the FTS of T-S fuzzy positive system. Our main works in this paper are as follows: 1) A new FTS criteria for studied system is established, since the FCLF is selected, our criterion is more general than [8][9][10]. 2) The upper bounds of TD of membership functions is considered, hence our results are less conservative.…”

A direct analysis method to globalh‐stability of delayed time‐varying nonlinear positive systems

“…Then h −1 is a positive-differentiable and monotonically increasing function, and hence g(t) ∶= d dt h −1 (t) is nonnegative. Let x(t) be an arbitrary solution of system (1). Then d dt…”

“…If the initial conditions of a dynamical system are nonnegative, then it is a positive system when its trajectory remains always in the positive quadrant. 1,2 Positive systems have been playing an important role when it comes to establishing the model of dynamical phenomena involving nonnegative variables, such as population level in ecology, concentration of substances in biology and chemistry, and absolute temperature in physics. 3,4 Therefore, in the past decades, the applications and analysis of positive systems have attracted worldwide attention (see References 5-12 and the references there in).…”

“…In this research, we looked into the global h‐stability of nonlinear positive systems with multiple time‐varying delays. If the initial conditions of a dynamical system are nonnegative, then it is a positive system when its trajectory remains always in the positive quadrant 1,2 . Positive systems have been playing an important role when it comes to establishing the model of dynamical phenomena involving nonnegative variables, such as population level in ecology, concentration of substances in biology and chemistry, and absolute temperature in physics 3,4 .…”