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 introduce the concept of sos-convex Lyapunov functions for stability analysis of both linear and nonlinear difference inclusions (also known as discrete-time switched systems). These are polynomial Lyapunov functions that have an algebraic certificate of convexity and that can be efficiently found via semidefinite programming. We prove that sos-convex Lyapunov functions are universal (i.e., ...

We present a novel method to compute Lyapunov functions for continuous-time systems with multiple local attractors. In the proposed method one first computes an outer approximation of the local attractors using a graphtheoretic approach. Then a candidate Lyapunov function is computed using a Massera-like construction adapted to multiple local attractors. In the final step this candidate Lyapuno...

In this paper we consider the stabilization of hybrid systems with both continuous and discrete dynamics via predictive control. To deal with the presence of discrete dynamics we adopt a “hybrid” control Lyapunov function approach, which consists of using two different functions. A Lyapunov-like function is designed to ensure finite-time convergence of the discrete state to a target value, whil...

The consistent Lyapunov methodology enables us, after its single application, to solve completely the asymptotic (or, exponential) stability problem, to construct a system Lyapunov function and to determine accurately the domain of asymptotic stability. This is achieved in the paper for invariant sets of non-differentiable time-varying non-linear systems. The results (proved in details) present...

We use discrete quadratic Lyapunov functions to design controllers for a class of systems where time intervals between state measurements are longer than time intervals between control actions and different components of the state vector are not measured at the same time. The discrete Lyapunov function is a discretization of a continuous Lyapunov function assumed to be known for the idealized s...