2010
DOI: 10.1016/j.sysconle.2010.01.002
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Stability radii for positive linear time-invariant systems on time scales

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Cited by 36 publications
(16 citation statements)
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“…The exponential stability of system (9) can be determined by the following criterion ( Doan et al., 2009 ): Every solution is exponentially stable if and only if all the eigenvalues of A have negative real parts. The solution of system (1) is of the following form ( Lawrence, 1991 ): where the first term on the right hand side of (10) is the solution to system (9); and the second term is an integral of function of A , B , V ( t ) and β 0 .…”
Section: Methodsmentioning
confidence: 99%
See 1 more Smart Citation
“…The exponential stability of system (9) can be determined by the following criterion ( Doan et al., 2009 ): Every solution is exponentially stable if and only if all the eigenvalues of A have negative real parts. The solution of system (1) is of the following form ( Lawrence, 1991 ): where the first term on the right hand side of (10) is the solution to system (9); and the second term is an integral of function of A , B , V ( t ) and β 0 .…”
Section: Methodsmentioning
confidence: 99%
“…It characterizes whether the solutions (trajectories) of a dynamic system is stable under small perturbations of the initial conditions. Over the past decades, many researchers have studied the stability of various kinds of dynamic systems, such as linear systems ( Lawrence, 1991 ), nonlinear systems ( Khalil and Grizzle, 2002 , Sastry, 1999 ), time-invariant systems ( Doan et al., 2009 , Pötzsche et al., 2003 ), time-varying systems ( DaCunha, 2005 , Hinrichsen et al., 1989 ) and systems with time-delay ( Gu et al., 2003 , Park, 2007 ). For a dynamic system with deterministic parameters, the stability is dichotomous and deterministic, i.e.…”
Section: Introductionmentioning
confidence: 99%
“…In [6], linear periodic systems of dynamic equations defined on a time scale of the same period were considered, and sufficient conditions for the asymptotic stability of systems of this class were established by using matrix-valued Lyapunov functions. In [7], linear systems of dynamic equations with constant matrix reducible to the Jordan form were considered, and conditions for the exponential stability of these systems were obtained.…”
Section: Introductionmentioning
confidence: 99%
“…[16,4]). The system x ∆ = Ax + Bu is positive if and only if all elements of A T and B are nonnegative.…”
mentioning
confidence: 99%