In the paper by Dashkovskiy, Ito, and Wirth the construction of Lyapunov functions for nonlinear composite systems is pursued. These systems consist of usually more than two interconnected subsystems for which input-to-state stability (ISS) Lyapunov functions are assumed to be known. Yet, so far, the stability of the overall system, or equivalently, the existence of a Lyapunov function for the ...

This paper deals with the controller design of the vehicle dynamics. In order to ensure the stability of the considered model, we propose an adaptive control law which forces the dynamics behavior to converge toward their equilibrium domain. This approach is based on the Lyapunov stability concept. The effectiveness of such scheme is illustrated by simulation results. Key wordNon linear systems...

This study presents a novel means of designing a simple and effective torque controller for Permanent Magnet Synchronous Motor (PMSM). The overall stability of the system is shown using Lyapunov technique. The Lyapunov functions used contain a term penalizing the integral of the tracking error, enhancing the stability. The tracking error is shown to be globally uniformly bounded. Simulation res...

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...

The problem of pth mean exponential stability and stabilizability of a class of stochastic nonlinear and bilinear hybrid systems with unstable and stable subsystems is considered. Sufficient conditions for the pth mean exponential stability and stabilizability under a feedback control and stabilizing switching rules are derived. A method for the construction of stabilizing switching rules based...

In this note, we study the relationship between the sample and moment Lyapunov exponents for jump linear systems. Using a large deviation theorem, a modified version of Arnold’s formula for connecting sample path and moment Lyapunov exponents for continuous-time linear stochastic systems is extended to discrete-time jump linear systems. Sample path stability properties of linear stochastic syst...

-This study addresses a fuzzy Lyapunov method for the stability analysis of time-delay fuzzy systems subject to external disturbances. The Takagi-Sugeno (T-S) fuzzy model and parallel distributed compensation (PDC) scheme are first employed to design a nonlinear fuzzy controller in order to stabilize the time-delay fuzzy systems. According to the controlled system, the H infinity criterion is d...

This paper presents an adaptive nonlinear position controller with velocity constraint, capable of combining the input-output linearization technique and Lyapunov stability theory. Based on the Lyapunov stability theory, the adaptation law of the proposed controller is derived along with the verification of the overall system’s stability. Computer simulation results demonstrate that the propose...

Stability and robustness issues for hybrid systems are considered in this paper. Present stability results, that are extensions of classical Lyapunov theory, are not straightforward to apply in general due to two reasons. First, existing theory do not unveil how to find needed Lyapunov functions. Secondly, at some time instants it is necessary to know the values of the continuous trajectory. Be...

The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, in particular, of stochastic differential systems. The main purpose of the paper is the analysis of the stability of stochastic differential equations by using Lyapunov functions when the origin is not necessarily an equilibrium point. The global uniform boundedness and th...