Lyapunov quadratic functionals are used to test the stability of systems, to compute the critical delay values for time delay systems, to compute the exponential estimates for the solutions of time delay systems, to calculate the robustness bounds for uncertain time delay systems, and to calculate a quadratic performance index for the process of parametric optimization for time delay systems. W...

In this paper, the problem of robust filter design for networked systems with time-varying sampling rate is investigated. The design conditions are obtained by using the Lyapunov theory and the Finsler’s Lemma. A robust filter, that minimizes an upper bound to the H∞ performance of the estimation error, is obtained as the solution of an optimization problem. A path-dependent Lyapunov function i...

In previous works, the authors introduced a framework for software analysis, which is based on optimization of Lyapunov invariants. These invariants prove critical software properties such as absence of overflow and termination in finite time. In this paper, graph models of software are introduced and the software analysis framework is further developed and extended on graph models. A distribut...

A generic parameterization of Lyapunov function candidates is suggested for a quite general class of non-autonomous smooth nonlinear systems. It is shown that conditions for the existence of a Lyapunov function that guarantees uniform exponential stability can be formulated as a set of linear matrix inequalities. Hence, computation of the Lyapunov function involves the solution of a convex opti...

This paper focuses on the design of control Lyapunov function for control affine systems to guarantee the stability for the states of interest in a specified region. Without restrictive assumptions found in previous approaches, a min-max optimization problem is formulated to solve for a quadratic Lyapunov function. A derivative-free coordinate search method is employed to optimize a non-differe...

This paper presents stability analysis and robust H∞ control for nonlinear switched systems bounded in sectors with arbitrary boundaries. By proposing new and more general multiple Lyapunov functions that incorporate nonlinearities in the system, we formulate the stability conditions under arbitrary switching in the form of linear matrix inequalities. Moreover, an optimization problem subject t...

This paper proposes a delay-dependent leader-following consensus condition of multi-agent systems with both communication delay and probabilistic self-delay. The proposed methods employ a suitable piecewise Lyapunov-Krasovskii functional and the average dwell time approach. New consensus criterion for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily ...

Several challenging problems of robust filtering are addressed in this paper. First of all, we exploit a new LMI (Linear Matrix Inequality) characterization of minimum variance or of H2 performance, and demonstrate that it allows the use of parameterdependent Lyapunov functions while preserving tractability of the problem. The resulting conditions are less conservative than earlier techniques w...

Based on a recent duality theory for linear differential inclusions (LDIs), the condition for stability of an LDI in terms of one Lyapunov function can be easily derived from that in terms of its conjugate function. This paper uses a particular pair of conjugate functions, the convex hull of quadratics and the maximum of quadratics, for the purpose of estimating the domain of attraction for sys...

This paper considers the problem of designing utility maximization scheduling algorithms for multi-channel(e.g, OFDM-based) wireless down-link systems. We extend Lyapunov Optimization to design a throughput-utility maximizing algorithm that uses a queue-based and delay-based Lyapunov functions, where the delay uses explicit delay information from the head-of-line packet destined to each user. O...