Phase-Based Gain-Modulation (PBGM) control is realized by modulating controller gains in response to the phase of the system state or tracking error. PBGM controllers have been applied to robotic hands, parallel manipulators and flexible mechanisms to give increased damping, reduced tracking error and friction compensation. A novel method is presented to establish Lyapunov stability for PBGM co...

In this paper we make a detailed numerical comparison between three algorithms for the computation of the full Lyapunov spectrum as well as the associated eigen-vectors of general dynamical systems. They are : (a) the standard method, (b) a differential formulation of the standard method, and (c) a new algorithm which does not require rescaling and reorthogonalization. We also bring out the rel...

A method for determination and two methods for approximation of the domain of attraction Da(0) of an asymptotically stable steady state of an autonomous, R-analytical, discrete system is presented. The method of determination is based on the construction of a Lyapunov function V , whose domain of analyticity is Da(0). The first method of approximation uses a sequence of Lyapunov functions Vp, w...

The fuzzy Lyapunov method is investigated for use with a class of interconnected fuzzy systems. The interconnected fuzzy systems consist of J interconnected fuzzy subsystems, and the stability analysis is based on Lyapunov functions. Based on traditional Lyapunov stability theory, we further propose a fuzzy Lyapunov method for the stability analysis of interconnected fuzzy systems. The fuzzy Ly...

Lyapunov design methods are used widely in control engineering to design controllers that achieve qualitative objectives, such as stabilizing a system or maintaining a system’s state in a desired operating range. We propose a method for constructing safe, reliable reinforcement learning agents based on Lyapunov design principles. In our approach, an agent learns to control a system by switching...

We address the problem of computing a low-rank estimate Y of the solution X of the Lyapunov equation AX + XA′ + Q = 0 without computing the matrix X itself. This problem has applications in both the reduced-order modeling and the control of large dimensional systems as well as in a hybrid algorithm for the rapid numerical solution of the Lyapunov equation via the alternating direction implicit ...

We discuss several techniques for the evaluation of the generalized Lyapunov exponents which characterize the growth of products of random matrices in the large-deviation regime. A Monte Carlo algorithm that performs importance sampling using a simple random resampling step is proposed as a general-purpose numerical method which is both efficient and easy to implement. Alternative techniques co...

In this paper, we discuss the synchronization and anti-synchronization of two identical chaotic T-systems. The adaptive and nonlinear control schemes are used for the synchronization and anti-synchronization. The stability of these schemes is derived by Lyapunov Stability Theorem. Firstly, the synchronization and anti-synchronization are applied to systems with known parameters, then to systems...

In this paper, we propose a Lyapunov function design method using a difference approximation scheme and quantization of the Markov process. First, we approximate a Lyapunov equation by a Schrödinger-like equation. Second, we obtain sufficient conditions for a function to be a Lyapunov function. Then, we provide a Lyapunov function design procedure.

The use of Lyapunov conditions for proving functional inequalities was initiated in [5]. It was shown in [4, 30] that there is an equivalence between a Poincaré inequality, the existence of some Lyapunov function and the exponential integrability of hitting times. In the present paper, we close the scheme of the interplay between Lyapunov conditions and functional inequalities by • showing that...