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).

This paper reviews the vast literature on static output feedback design for linear time-invariant systems including classical results and recent developments. In particular, we focus on static output feedback synthesis with performance specifications, structured static output feedback, and robustness. The paper provides a comprehensive review on existing design approaches including iterative li...

Abslraet-Recent applications of absolute stability methods to robustness analysis have led to a rebirth of interest in this topic. This paper is concerned with the robust stability of feedback distributed parameter systems against nonlinear and random disturbances. Our analysis is based on the Lyapunov direct method. To derive a stochastic Lyapunov function, we introduce the special stochastic ...

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...

in this paper standing balance control of a biped with toe-joint is presented. the model consists of an inverted pendulum as the upper body and the foot contains toe-joint. the biped is actuated by two torques at ankle-joint and toe-joint to regulate the upper body in upright position. to model the interaction between foot and the ground, configuration constraints are defined and utilized. to s...

Cellular Automata are simple computational models which can be leveraged to model a wide variety of dynamical systems. Composed of a lattice of discrete cells that take finite number of states based on previous iterations these models differ greatly from dynamic systems that vary continuously in space or time. However given their ability to model many of continuous systems, it could be postulat...