On linear co-positive Lyapunov functions for sets of linear positive systems

Abstract

In this paper we derive necessary and sufficient conditions for the existence of a common linear co-positive Lyapunov function for a finite set of linear positive systems. Both the state dependent and arbitrary switching cases are considered. Our results reveal an interesting characterisation of "linear" stability for the arbitrary switching case; namely, the existence of such a linear Lyapunov function can be related to the requirement that a number of extreme systems are Metzler and Hurwitz stable. Examples are given to illustrate the implications of our results.

Mixed l −/l 1 fault detection observer design for positive switched systems with time-varying delay via delta operator approach

“…Definition 6: Given positive switched delta operator system (1), for two positive scalars γ and β, the observer (5) is said to be an l -/l 1 fault detection observer if 1) Error system (6) is exponentially stable when ( ) 0 w k = and ( ) 0; f k = 2) Under zero initial conditions, (9) and (10) hold.…”

“…It should be pointed out that a linear co-positive Lyapunov functional is powerful for the analysis and synthesis of positive systems [7]. Some results on the stability and stabilization of such systems have been obtained in [8,9]. It has been shown that the l 1 performance index can characterize effectively the disturbance attenuation performance because of the peculiar nonnegative property of positive systems [10,11].…”

Common Weak Linear Copositive Lyapunov Functions for Positive Switched Linear Systems

“…It is well known that the existence of CLCLFs implies asymptotic stability of PSLSs under arbitrary switching. Moreover, necessary and sufficient conditions for the existence of CLCLFs have been extensively investigated in [18][19][20][21][22].…”

Positive $$L_1 $$ L 1 Observer Design for Positive Switched Systems

“…Recently, positive switched systems have been highlighted and investigated by many researchers due to the broad applications in communication systems [30,31], formation flying [11], the viral mutation dynamics under drug treatment [21] and systems theories [1,13,14,27,28]. However, it should be pointed out that to obtain some results on positive switched systems, one has to combine both features of general switched systems and positive systems [3,4,6,15,16,22,26].…”