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...

We consider the class of closed generic fluid networks (GFN) models, which provides an abstract framework containing a wide variety of fluid networks. Within this framework a Lyapunov method for stability of GFN models was proposed by Ye and Chen. They proved that stability of a GFN model is equivalent to the existence of a functional on the set of paths that is decaying along paths. This resul...

This paper presents a new stability and L2-gain analysis of linear Networked Control Systems (NCS). The new method is inspired by discontinuous Lyapunov functions that were introduced by Naghshtabrizi et al. (Syst. Control Lett. 2008; 57:378–385; Proceedings 26th American Control Conference, New York, U.S.A., July 2007) in the framework of impulsive system representation. Most of the existing w...

Rapid state control of quantum systems is significant in reducing the influence of relaxation or decoherence caused by the environment and enhancing the capability in dealing with uncertainties in the model and control process. Bang-bang Lyapunov control can speed up the control process, but cannot guarantee convergence to a target state. This paper proposes two classes of new Lyapunov control ...

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...

Low-rank iterative methods of periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems Low-rank iterative methods of periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems Abstract We discuss the numerical solution of large-scale sparse projected discrete-time periodic Lyapunov equations ...

We introduce a “spatial” Lyapunov exponent to characterize the complex behavior of non chaotic but convectively unstable flow systems. This complexity is of spatial type and is due to sensitivity to the boundary conditions. We show that there exists a relation between the spatial-complexity index we define and the comoving Lyapunov exponents. In these systems the transition to chaos, i.e. the a...

For discrete-time descriptor syslems, various generalized Lyapunov equations were studied in the literature. Howevn these well known generalized Lyapunov equations can be used only under some restrictive assumptions on the plant (as system regularity, or positiveness of a Q matrix, for example). To overcome these limitations, we propose in this paper a new generalized Lyapunov equation for disc...

We consider a finite number of nonlinear systems interconnected in an arbitrary way. Under the assumption that each subsystem is input-to-state stable (ISS) regarding the states of the other subsystems as inputs we are looking for conditions that guarantee input-to-state stability of the overall system. To this end we aim to construct an ISS-Lyapunov function for the interconnection using the k...

In this paper, we use a state-dependent Lyapunov function to reduce the conservatism in stability analysis of Takagi-Sugeno (T-S) fuzzy systems via Linear Matrix Inequalities (LMIs). Our approach uses T-S fuzzy rules to deene Lyapunov functions, and therefore substantially enlarges the class of Lyapunov functions which can be used to prove stability of T-S fuzzy systems. This approach greatly r...