On the Lyapunov and Bohl exponent of time-varying discrete linear system

Abstract

This note studies the problem of bounds for the Lyapunov exponent of a parameter perturbed system when the perturbation has finite average value. Such a bound is presented in terms of Bohl exponent of the unperturbed system. In particular, it has been shown that the Lyapunov exponent of perturbed system is not greater than the Bohl exponent of the unperturbed system if the average value of perturbations is zero. The obtained result is illustrated by a numerical example.

Resilient Corner-Based Vehicle Velocity Estimation

“…Choosing T = diag(γ, 1) with a design parameter γ > 0, leads toĀ eq whose stability margin, SM q max i λ i (Ā eq ), is close to the stability margin of its symmetric part (which will be discussed in Example 1 later). Moreover, due to the fact that ||T|| and ||T −1 || are bounded, the transformation matrix T preserves the exponential stability and the exponent (rate) of the convergence [31], [32]. The Lyapunov candidate V(ē q (t)) = 1 2ē q (t) Tē q (t) is then introduced to investigate the stability of the error dynamics (8) and (13) 2 .…”

Positivity and stability of fractional descriptor time–varying discrete–time linear systems

“…The Lyapunov, Bohl and Perron exponents as well as stability of time-varying discrete-time linear systems were investigated by Czornik (2014), Czornik et al (2012;, Czornik and Niezabitowski (2013a;2013b;2013c) as well as Niezabitowski (2014). Positive standard and descriptor systems and their stability were analyzed by Kaczorek (2001;2011;1998a;2015b), along with positive linear systems with different fractional orders (Kaczorek, 2011;2012) and singular discrete-time linear systems (Kaczorek, 1998a;2015a).…”

Analysis of positivity and stability of fractional discrete-time nonlinear systems

“…Models having positive behavior can be found in engineering, economics, social sciences, biology and medicine, etc. The Lyapunov, Bohl and Perron exponents and stability of time-varying discrete-time linear systems have been investigated in [1][2][3][4][5][6][7]. The positive standard and descriptor systems and their stability have been analyzed in [15][16][17][18][19][20].…”