Stability of periodically switched discrete-time linear singular systems

Stability of arbitrarily switched discrete-time linear singular systems of index-1

“…From condition (ii) in Definition 1 we show that ker R , {1,2,.., }. Using similar arguments as in [8][9][10][11] we can prove the following results. Theorem 1 For index-1 SDLS (1), the following assertions hold.…”

A Comparison Theorem for Stability of Linear Stochastic Implicit Difference Equations of Index-1

“…ii are used for the index-1 concept for implicit difference equations, see [15][16][17]. This natural restriction…”

The one-step-map for switched singular systems in discrete-time

“…We consider switched singular systems (SwSS) in discrete time of the form E σ(k) x(k + 1) = A σ(k) x(k) + B σ(k) u(k), k ∈ N, (1) where σ : N → {1, 2, . .…”

“…the presence of a switch results in the loss of unique solvability. // The loss of causality and uniqueness due to switching is usually an undesired property and our goal is to give conditions for well-posedness of the switched system (1) in the sense that a family of one-step-maps Φ i,j ∈ R n×n , i, j ∈ {1, 2, . .…”

“…Although some authors have already studied discrete-time singular switched (or time-varying) systems (e.g. [15], [2], [16], [3], [26], [29], [31], [28], [6], [7], [27], [1]) it seems that the existence of a one-step-map was not investigated so far and we want to close this gap with this contribution.…”