This paper introduces a new method for proving global stability of fluid flows through the construction of Lyapunov functionals. For finite dimensional approximations of fluid systems, we show how one can exploit recently developed optimization methods based on sum-of-squares decomposition to construct a polynomial Lyapunov function. We then show how these methods can be extended to infinite di...

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...

The discrete-time periodic Lyapunov equation has several important applications in the analysis and design of linear periodic control systems. Specific applications considered in the paper are the solution of stateand output-feedback optimal periodic control problems, the stabilization by periodic state feedback and the square-root balancing of discrete-time periodic systems. Efficient numerica...

Robust stability analysis of uncertain discrete time systems is studied. The LMI robust stability analysis method based on polynomial parameter dependent Lyapunov function is presented. This method is compared with other robust stability analysis methods formulated through LMI using linear parameter dependent Lyapunov function. The results are tested on randomly generated examples.

This paper deals with the analysis and design of the state feedback fuzzy controller for a class of discrete time Takagi -Sugeno (T-S) fuzzy uncertain systems. The adopted framework is based on the Lyapunov theory and uses the linear matrix inequality (LMI) formalism. The main goal is to reduce the conservatism of the stabilization conditions using some particular Lyapunov functions. Four nonqu...

The ergodic properties of SDEs, and various time discretizations for SDEs, are studied. The ergodicity of SDEs is established by using techniques from the theory of Markov chains on general state spaces. Application of these Markov chain results leads to straightforward proofs of ergodicity for a variety of SDEs, in particular for problems with degenerate noise and for problems with locally Lip...

This paper studies the system stability problems of a class of nonconvex differential inclusions. At first, a basic stability result is obtained by virtue of locally Lipschitz continuous Lyapunov functions. Moreover, a generalized invariance principle and related attraction conditions are proposed and proved to overcome the technical difficulties due to the absence of convexity. In the technica...

In this paper we deal with the problem of computing Lyapunov functions for stability verification of differential systems. We concern on symbolic methods and start the discussion with a classical quantifier elimination model for computing Lyapunov functions in a given polynomial form, especially in quadratic forms. Then we propose a new semi-algebraic method by making advantage of the local pro...

Iterative learning control methods are represented as powerful tools to control dynamics nowadays. Our new controller based on particular case of iterative learning control is radically different from the presented conventional method, which attempts to stabilize a class of nonlinear systems by satisfying the conditions of Lyapunov Stability Theorem. Since our algorithm is model based, its robu...

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...