The paper presents a new method for higher order sliding mode control using control Lyapunov function for chain of integrator system with nonlinear uncertainties. The stability proof of the suggested scheme is analyzed in terms of two Lyapunov functions using appropriate switching function. Using these Lyapunov functions and switching scheme it is proved that, output and its higher order deriva...

In this paper we consider stabilization of switching nonlinear systems represented by TS models. To develop the conditions we use two different switching Lyapunov functions. For each Lyapunov function a set of conditions is developed. The conditions are formulated as LMIs and relaxed using delays in the controller and the Lyapunov function. The application of the conditions is illustrated on nu...

The relation between the Lyapunov modes (delocalized Lyapunov vectors) and the momentum autocorrelation function is discussed in two-dimensional hard-disk systems. We show numerical evidence that the smallest time-oscillating period of the Lyapunov modes is twice as long as the time-oscillating period of momentum autocorrelation function for both square and rectangular two-dimensional systems w...

This paper presents an alternative approach for obtaining a converse Lyapunov theorem for discrete-time systems. The proposed approach is constructive, as it provides an explicit Lyapunov function. The developed converse Lyapunov theorem establishes existence of global Lyapunov functions for globally exponentially stable (GES) systems and for globally asymptotically stable systems, Lyapunov fun...

We consider the first order periodic systems perturbed by a 2N × 2N matrix-valued periodic potential on the real line. The spectrum of this operator is absolutely continuous and consists of intervals separated by gaps. We define the Lyapunov function, which is analytic on an associated N-sheeted Riemann surface. On each sheet the Lyapunov function has the standard properties of the Lyapunov fun...

We investigate the index sets associated with the degree structures of computable sets under the parameterized reducibilities introduced by the authors. We solve a question of Peter Cholak and the first author by proving the fundamental index sets associated with a computable set A, {e : We ≤q A} for q ∈ {m, T } are 0 4 complete. We also show that FPT (≤q), that is {e : We computable and ≡q ∅},...

In this paper, finite-time adaptive consensus problem is investigated for first-order multiagent systems with unknown nonlinear dynamics. Linearly parameterized method is introduced to model unknown nonlinear dynamics of the systems. By only utilizing the local relative position state information between each agent and its neighbors, decentralized finite-time adaptive consensus algorithms are p...

We present a verification methodology for cooperating traffic agents covering analysis of cooperation strategies, realization of strategies through control, and implementation of control. For each layer, we provide dedicated approaches to formal verification of safety and stability properties of the design. The range of employed verification techniques invoked to span this verification space in...

This report develops an ensemble or statistical eddy viscosity model. The model is parameterized by an ensemble of solutions of an ensemble-Leray regularization. The combined approach of ensemble time stepping and ensemble eddy viscosity modeling allows direct parametrization of the turbulent viscosity coefficient that gives an unconditionally stable algorithm. We prove that the model’s solutio...

In this paper, a design problem of dynamic output feedback controller for asymptotic stabilization of a class of uncertain neutral systems with input delay has been investigated. A criterion for the existence of such controllers is derived based on the LMI (linear matrix inequality) approach combined with the Lyapunov method. A parameterized characterization of the controllers is given in terms...