Stability of switched positive descriptor systems with average dwell time switching

Abstract

In this paper, the problems of stability for a class of switched positive descriptor systems (SPDSs) with average dwell time (ADT) switching are investigated. First, based on the equivalent switched system and the properties of the projector matrix, sufficient stabilities are given for the underlying systems in both continuoustime and discrete-time contexts. Then, a sufficient stability condition for the SPDS with both stable and unstable subsystems is obtained. The stability results for the SPDSs are represented in terms of a set of linear programmings (LPs) by the multiple linear co-positive Lyapunov function (MLCLF) approach. Finally, three numerical examples are given to illustrate the effectiveness of the obtained theoretical results.

Finite-Time Stability of Discrete Linear Singular Switched Positive Systems with Time-Delay by a Mode-Dependent Average Dwell Time Approach

“…Therefore, the MDADT switching law is more suitable in practice than the ADT switching law [37,41]. To deal with such situations, in [31], the authors studied the stability for a class of singular switched positive systems with ADT switching law, but the time-delay was not considered. In [12], the problems of stability, l 1 -gain and l ∞ -gain analysis for discrete singular switched positive systems with time-delay were investigated.…”

Global Exponential Stability and Stabilization of Fractional-Order Positive Switched Systems

“…Many remarkable results related to positive switched systems have been presented, see [1][2][3][4][5][6] and references therein. These results mentioned above refer to the positive switched systems with integer order derivative.…”

On l1 stability of switched positive singular systems with time‐varying delay

“…There are only a few recent publications investigating SPSSs . In , the problems of stability for a class of switched positive descriptor systems with average dwell time switching were investigated.…”

“…There are only a few recent publications investigating SPSSs . In , the problems of stability for a class of switched positive descriptor systems with average dwell time switching were investigated. Reference dealt with the problem of state feedback controller design for singular positive Markovian jump systems with partly known transition rates.…”

“…Reference dealt with the problem of state feedback controller design for singular positive Markovian jump systems with partly known transition rates. However, both only focused on the autonomous case without taking time delay and exogenous disturbance into account. As time delay and exogenous disturbance are frequently encountered in practice, it is necessary and significant to further investigate SPSSs with those two kinds of phenomena.…”