On new estimates for Lyapunov exponents of discrete time varying linear systems

Alternative formulae for lower general exponent of discrete linear time-varying systems

“…Denote by Φ D (n, m) , Ψ D (n, m) the transition matrices of (31) and (32), respectively. By (15) for any ε > 0 we may find T, m ∈ N such that…”

“…Applications of the Bohl exponents to the discrete switched linear systems is presented in [30]. Moreover, Bohl exponents have been also successfully used to derive robustness results for linear time-varying difference equations [31]. For an excellent summary of the history of the development of Lyapunov and Bohl exponents see ( [32], pp.…”

On the number of upper Bohl exponents for diagonal discrete time-varying linear system

“…Perron exponents, which are closely related to them, appeared for the first time in [61] and [62]. Both of them were introduced in the context of linear time-varying differential equations and since then, they are an object of intensive research both for continuous-time and discrete-time, have many generalizations and variants (see [1][2][3][4][5][6][9][10][11][12][16][17][18]20,21,[23][24][25][26][27][28][29][30][31][32][33][34][35][36][40][41][42][43][44][45]49,52,53,69]). Moreover, the problem of sensitivity to parameter variation has been widely investigated (see for example [31] and the references therein).…”

Stability and controllability of switched systems

“…There are several approaches to defining the exponential growth rate, all of which turn out to be equivalent. A trajectory based definition considers Lyapunov exponents [36][37][38][39][40][41][42][43][44][45][46][47][48] of individual trajectories, which are defined in the discrete-time case as…”

“…The quantity ln ρ(d) is known in the control theory literature as the greatest Lyapunov exponent. Properties of Lyapunov exponents were studied in [37][38][39][40][41][42][43][44][45][46][47][48][49][50][51], where sufficient conditions so that Lyapunov exponents characterizes exponential stability for switched systems are shown. In particular, it was shown that the system (1) is absolutely stable if and only if sup…”