Title of dissertation: LINEAR STABILITY ANALYSIS USING LYAPUNOV INVERSE ITERATION Minghao Wu, Doctor of Philosophy, 2012 Dissertation directed by: Professor Howard Elman Department of Computer Science Institute for Advanced Computer Studies In this dissertation, we develop robust and efficient methods for linear stability analysis of large-scale dynamical systems, with emphasis on the incompres...

In this paper we study the exponential and uniform exponential stability problem for linear discrete time-varying systems with independent stochastic perturbations. We give two representations of the solutions of the discussed systems and we use them to obtain necessary and sufficient conditions for the two types of stability. A deterministic characterization of the uniform exponential stabilit...

In the present work a discontinuous control law for chained systems of order n that yields global asymptotic regulation and local exponential stability in the sense of Lyapunov is proposed. As a consequence of the Lyapunov stability property the new control law assures robustness against the e ect of (small) measurement noise and of external disturbances. Simulation results complement the theor...

This note presents a stability analysis method for piecewise discrete-time linear systems based on a piecewise smooth Lyapunov function. It is shown that the stability of the system can be established if a piecewise Lyapunov function can be constructed and, moreover, the function can be obtained by solving a set of linear matrix inequalities (LMIs) that is numerically feasible with commercially...

This paper investigates stability of interconnection of integral input-to-state stable (iISS) systems. A new tool to verify the stability is proposed by focusing on Lyapunov inequalities each system is to satisfy in accordance with a small-gain-type condition. The purpose of this paper is to extend the technique of “flexible Lyapunov inequalities” developed previously for input-to-state stable(...

An efficient technique namely Backpropagation training with adaptive parameters using Lyapunov Stability Theory for training single hidden layer feed forward network is proposed. A three-layered Feedforward neural network architecture is used to solve the selected problems. Sequential Training Mode is used to train the network. Lyapunov stability theory is employed to ensure the faster and stea...

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 properties as Lyapunov functions. We give tools for designing composite filtered Lyapunov functions for cascaded systems. These functions are used to design globally...

In this paper, the stability of switched linear systems is investigated using piecewise linear Lyapunov functions. In particular, we identify classes of switching sequences that result in stable trajectories. Given a switched linear system, we present a systematic methodology for computing switching laws that guarantee stability based on the matrices of the system. In the proposed approach, we ...

In practice, one is not only interested in the qualitative characterizations provided by the Lyapunov stability, but also in quantitative information concerning the system behavior, including estimates of trajectory bounds, possibly over finite time intervals. This type of information has been ascertained in the past in a systematic manner using the concept of practical stability. In the presen...