TY - JOUR

T1 - On Diagonal Stability of Positive Systems with Switches and Delays

AU - Aleksandrov, A. Yu

AU - Mason, O.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - We consider linear positive systems with delay and switchings of operation modes. We establish conditions under which it is possible to construct a common Lyapunov–Krasovskii diagonal functional for the family of subsystems corresponding to the system with switchings in consideration. These conditions are formulated in terms of the feasibility of auxiliary systems of linear algebraic inequalities. In addition, we study the problem of the existence of a diagonal functional of a special form. We also show that our results can be used to analyze the stability of some classes of nonlinear positive systems with delay.

AB - We consider linear positive systems with delay and switchings of operation modes. We establish conditions under which it is possible to construct a common Lyapunov–Krasovskii diagonal functional for the family of subsystems corresponding to the system with switchings in consideration. These conditions are formulated in terms of the feasibility of auxiliary systems of linear algebraic inequalities. In addition, we study the problem of the existence of a diagonal functional of a special form. We also show that our results can be used to analyze the stability of some classes of nonlinear positive systems with delay.

KW - delays

KW - diagonal stability

KW - linear inequalities

KW - positive system

KW - switching systems

UR - http://www.scopus.com/inward/record.url?scp=85058350305&partnerID=8YFLogxK

U2 - 10.1134/S0005117918120020

DO - 10.1134/S0005117918120020

M3 - Article

AN - SCOPUS:85058350305

VL - 79

SP - 2114

EP - 2127

JO - Automation and Remote Control

JF - Automation and Remote Control

SN - 0005-1179

IS - 12

ER -