This paper presents a new approach for the stability analysis of TakagiSugeno (T-S) fuzzy systems. An idea is investigated to use piecewise quadratic Lyapunov function with low amount of computations. This class of Lyapunov function candidates is much richer than the common quadratic Lyapunov function. By exploiting the piecewise continuous Lyapunov function, we derive stability conditions that...

As is widely recognized in Lyapunov analysis, linearized Hamilton's equations of motion have two marginal directions for which the Lyapunov exponents vanish. Those directions are the tangent one to a Hamiltonian flow and the gradient one of the Hamiltonian function. To separate out these two directions and to apply Lyapunov analysis effectively in directions for which Lyapunov exponents are not...

Almost sure asymptotic stability of stochastic difference and differential equations with non-anticipating memory terms is studied in R. Sufficient criteria are obtained with help of Lyapunov-Krasovskǐi-type functionals, martingale decomposition and semi-martingale convergence theorems. The results allow numerical methods for stochastic differential equations with memory to be studied in terms ...

Lyapunov drift is a powerful tool for optimizing stochastic queueing networks subject to stability. However, the most convenient drift conditions often provide results in terms of a time average expectation, rather than a pure time average. This paper provides an extended drift-plus-penalty result that ensures stability with desired time averages with probability 1. The analysis uses the law of...

in this paper, under the existence of system uncertainties, external disturbances, and input nonlinearity, global finite time synchronization between two identical attractors which belong to a class of second-order chaotic nonlinear gyros are achieved by considering a method of continuous smooth second-order sliding mode control (hoamsc). it is proved that the proposed controller is robust to m...

this work proposes a neural-fuzzy sliding mode control scheme for a hydro-turbine speed governor system. considering the assumption of elastic water hammer, a nonlinear mode of the hydro-turbine governor system is established. by linearizing this mode, a sliding mode controller is designed. the linearized mode is subject to uncertainties. the uncertainties are generated in the process of linear...

An iterative method for the low-rank approximate solution of a class of generalized Lyapunov equations is studied. At each iteration, a standard Lyapunov is solved using Galerkin projection with an extended Krylov subspace method. This Lyapunov equation is solved inexactly, thus producing a nonstationary iteration. Several theoretical and computational issues are discussed so as to make the ite...

This paper proposes a recursive method of constructing weak-control-Lyapunov functions for nonlinear systems. Lyapunov function is one of effective tools to study stability and stabilization in nonlinear system control design. However, a general way of finding Lyapunov functions has not been known yet. Our method is introduced by an explicit topological-geometric assumption for a state space ma...

The Lyapunov stability method is the most popular and applicable stability analysis tool of nonlinear dynamic systems. However, there are some bottlenecks in the Lyapunov method, such as need for negative definiteness of the Lyapunov function derivative in the direction of the system’s solutions. In this paper, we develop a new theorem to dispense the need for negative definite-ness of Lyapunov...

Some new Lyapunov type theorems for stochastic difference equations with continuous time are proven. It is shown that these theorems simplify an application of Lyapunov functionals construction method.