This paper presents an alternative approach for obtaining a converse Lyapunov theorem for discrete-time systems. The proposed approach is constructive, as it provides an explicit Lyapunov function. The developed converse Lyapunov theorem establishes existence of global Lyapunov functions for globally exponentially stable (GES) systems and for globally asymptotically stable systems, Lyapunov fun...

We provide necessary and sucient conditions for psi-conditional as-ymptotic stability of the solution of a linear matrix Lyapunov system and sucientconditions for psi -conditional asymptotic stability of the solution of a rst ordernon-linear matrix Lyapunov system X0 = A(t)X + XB(t) + F(t;X).

In this paper we introduce a generalized class of filtered Lyapunov functions, which are Lyapunov functions with time-varying parameters satisfying certain differential equations. Filtered Lyapunov functions have the same stability and robustness properties of Lyapunov functions. On the other hand, filtered Lyapunov functions can be easily handled to construct composite filtered Lyapunov functi...

4 Lyapunov Exponents 5 4.1 Definition and basic properties . . . . 6 4.2 Constraints on the Lyapunov exponents 7 4.3 Calculating the largest Lyapunov exponent method 1 . . . . . . . . . . . 7 4.4 Calculating the largest Lyapunov exponent method 2 . . . . . . . . . . . 8 4.4.1 Maps . . . . . . . . . . . . . . 8 4.4.2 Continuous systems . . . . . . 8 4.5 Calculating the other Lyapunov exponents ....

The construction of an input-to-state stability (ISS) Lyapunov function for networks of ISS system will be presented. First we construct ISS Lyapunov functions for each strongly connected component, then what remains is a cascade (or disconnected aggregation) of these strongly connected components. Using known results the constructed Lyapunov functions can be aggregated to one single ISS Lyapun...

comnode classification within membrane residue curves (m-rcms) currently hinges on lyapunov’s theorem and therefore the computation of mathematically complex eigenvalues. this paper presents an alternative criterion for the classification of nodes within m-rcms based on the total membrane flux at node compositions. this paper demonstrates that for a system exhibiting simple permeation behaviour...