Set of possible values of maximal Lyapunov exponents of discrete time-varying linear system

Estimation of the Joint Spectral Radius

“…This concept may be defined in several ways and even in the finite-dimensional case these different concepts are not equivalent. The joint spectral radius and subradius are closely connected to Lyapunov exponents of (3), see [13,[15][16][17][18][19], and Bohl exponents, see [1,11,14,21,43,44]. The following theorem contains the relation between the joint spectral radius and absolute stability of DLI (Σ).…”

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…”