Abstract
This paper investigates 1-moment exponential stability and exponential mean-square stability (EMS stability) under average dwell time (ADT) and the preset deterministic switching mechanism of dual switching linear continuous-time positive systems when a numerical realization does not exist. The signs of subsystem matrices, but not their structures of magnitude, are key information that causes a qualitative concept of stability called sign stability. Both 1-moment exponential stability and EMS stability, which are the traditional stability concepts, are generalized intrinsically. Hence, both 1-moment exponential sign stability and EMS sign stability are introduced and are proven based on sign equivalency. It is shown that they are symmetrically and qualitatively stable. Notably, the notion of stability can be checked quantitatively using some examples.
Highlights
Hybrid systems, which are classified based on probabilistic behavior and different driving switching mechanisms, are employed in a wide range of implementations
The paper analyzes 1-moment exponential and exponentially mean-square (EMS) sign stability of dual switching linear continuous-time positive systems (DSLCTPSs), which depend upon the average dwell time (ADT) and the predetermined deterministic switching strategy
The derivation of the sufficient stability condition in the form of LMI are reached in this research. 1-moment exponential stability cannot inevitably imply EMS stability
Summary
Hybrid systems, which are classified based on probabilistic behavior and different driving switching mechanisms, are employed in a wide range of implementations. The sign stability of dual switching linear positive systems (DSLPSs) is verified by the current research, its main contributions are: (i) the extraction of sufficient conditions so the stability of a DSLPS is guaranteed; (ii) 1-moment exponential sign stability and EMS sign stability of DSLPSs are verified. The paper analyzes 1-moment exponential and EMS sign stability of dual switching linear continuous-time positive systems (DSLCTPSs), which depend upon the ADT and the predetermined deterministic switching strategy. The sign stability analysis of DSLPS cannot be utilized by the previous strategy since each subsystem matrix is stable, which is not enough and is not necessary for the stability of DSLPSs. The equivalence between the stability of DSLPSs and particular matrices through LMI are designated by our results that are similar to our previous research. Qualitative results can be of merit and an intuitive complement to conventional numerically based methods could be employed for robust stability analysis
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