L₁‐Gain Analysis and Control for Switched Positive Systems with Dwell Time Constraint

Abstract

This paper studies the problems of L1‐gain analysis and control for switched positive systems with dwell time constraint. The state‐dependent switching satisfies a minimal dwell time constraint to avoid possible arbitrary fast switching. By constructing multiple linear co‐positive Lyapunov functions, sufficient conditions of stability and L1‐gain property are derived under the proposed switching strategy. Then, an effective state feedback controller is designed to ensure the positivity and L1‐gain property of the closed‐loop system. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

Robust finite‐time control and estimation for uncertain time‐delayed switched systems by observer‐based sliding mode technique

“…Comparing with the results in Reference 6, it reaches zero in 12 seconds; we can see from Figure 5 that the trajectory of x T ( t ) Rx ( t ) reaches zero in 2 seconds; it means that the designed method in this article makes the system state reach zero faster, in other words, the results of this article have better transient characteristics.…”

“…An example of the water quality control system is given to demonstrate the effectiveness of the proposed method. The water quality control system 5,6,37 can be attributed to interference attenuation analysis and synthesis problems. In this article, we consider a water quality model with two‐mode and third‐order state vectors, which expresses the algae, the ammonia production, and the dissolved oxygen content.…”

“…It consists of a class of subsystems and a description of the rules for switching relationships between subsystems. Switched system can used to describe some real processes with a wide range of applications, such as motor systems, 2 network control systems, 3 robot control systems, 4 and water‐quality systems 5-6 . A significant feature of switched system is that when all subsystems are stable, the designed switching signal does not necessarily guarantee the stability.…”

Necessary and Sufficient Stability Criterion and Stabilization for Positive 2‐D Continuous‐Time Systems with Multiple Delays

“…absolute temperature, concentrations of substances and population levels. Such a class of systems are referred as positive systems, whose output signal and the state variables are restricted in the first quadrant instead of the whole state space for nonnegative initial condition and the input signal . This typical nature of the positive systems makes the analysis and synthesis problems more interesting and challenging.…”

Estimation of stability region for discrete‐time linear positive switched systems with multiple equilibrium points

“…In recent years, the model of PSS has been broadly applied in computer science, biology, mechanical engineering and so on. More and more scholars are paying close attention to the stability of PSS, see [4,5,6,7,8,9]. Consequently, the approaches of common copositive Lyapunov function [10,11,12,13,14] and multiple copositive Lyapunov function [15,16,17] were proposed to study the stability of PSS.…”