Diagonal Invariance and Comparison Methods (original) (raw)
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Time-Dependent Invariant Sets in System Dynamics
Proceedings of the 2006 IEEE International Conference on Control Applications, 2006
The paper provides new results on the flow (positive) invariance of the families of 0-symmetrical sets, which are defined by arbitrary Hölder norms and time-dependent diagonal matrices. Thus, we introduce the concept of “diagonal invariance” as a system property with local or global character. For this property, we formulate sufficient conditions in the case of time-variant or -invariant, nonlinear systems
2002
For a class of uncertain nonlinear systems (UNSs), the flow-invariance of a timedependent rectangular set (TDRS) defines individual constraints for each component of the state-space trajectories. It is shown that the existence of the flowinvariance property is equivalent to the existence of positive solutions for some differential inequalities with constant coefficients (derived from the state-space equation of the UNS). Flow-invariance also provides basic tools for dealing with the componentwise asymptotic stability as a special type of asymptotic stability, where the evolution of the state variables approaching the equilibrium point (EP){0} is separately monitored (unlike the standard asymptotic stability, which relies on global information about the state variables, formulated in terms of norms). The EP{0} of a given UNS is proved to be componentwise asymptotically stable if and only if the EP{0} of a differential equation with constant coefficients is asymptotically stable in th...