General aggregation of large-scale systems by-vector Lyapunov functions and vector norms

Discontinuous Systems

“…Viewing V (Ω ) = |Ω | = |Ω 1 | |Ω 2 | as a vector Lyapunov function [28,87], the right-hand side Dini derivative of V (Ω ) satisfies…”

Stability and stabilization studies for a class of switched nonlinear systems via vector norms approach

“…Indeed, by constructing an appropriated common Lyapunov function [18][19][20], as well by using the vector norms notion [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] and also by resorting to the Kotelyanski lemma [38], the M Àmatrix proprieties [39,40], the aggregation techniques [34] and the application of the Borne-Gentina criterion [34,36], new sufficient stability conditions under arbitrary switching for the autonomous system are deduced. Then, these results are extended for designing a state feedback controller by using pole assignment control, which guarantee that the corresponding closed-loop system is globally asymptotically stable under arbitrary switching.…”

On Robust Stability Analysis of Uncertain Discrete-Time Switched Nonlinear Systems with Time Varying Delays

“…This paper seeks new algebraic practical stability criteria. Firstly, a novel robust asymptotic stability criterion for a class of discrete-time switched nonlinear systems with time varying delays and subject to polytopic uncertainties is established via constructing a new common Lyapunov functional [9], according to the vector norm notion [9][10][11][12][13][27][28][29][30][31] and M -matrix properties [32]. Secondly, the derived results are extended for a class of switched systems given by a set of difference equations.…”