Globally Exponentially Stable Research Articles

Absolute exponential stability of neural networks with a general class of activation functions

The authors investigate the absolute exponential stability (AEST) of neural networks with a general class of partially Lipschitz continuous (defined in Section II) and monotone increasing activation functions. The main obtained result is that if the interconnection matrix T of the network system satisfies that -T is an H-matrix with nonnegative diagonal elements, then the neural network system is absolutely exponentially stable (AEST); i.e., that the network system is globally exponentially stable (GES) for any activation functions in the above class, any constant input vectors and any other network parameters. The obtained AEST result extends the existing ones of absolute stability (ABST) of neural networks with special classes of activation functions in the literature.

Global Uniform Asymptotic Stability of Cascaded Non-autonomous Non-linear Systems: Application to Stabilisation of a Diesel Engine

In this paper, we deal with the stability analysis problem of cascaded non-autonomous non-linear systems. In particular, we answer to the following questions: (i) What happens with the solutions of a time-varying non-linear system which is globally uniformly stable (GUS), when it is perturbed by the output of a globally exponentially stable (GES) system, in particular, when both systems form a cascade? (ii) If a time-varying non-linear system is globally uniformly asymptotically stable (GUAS), is this stability properly preserved when it is perturbed by an exponentially decaying input? Our proofs are based on a standard ‘delta-epsilon’ Lyapunov analysis. Finally, we show the utility of our results by applying our theorems to the problem of stabilisation of a turbo-charged diesel engine.

Nonlinear output feedback control of dynamically positioned ships using vectorial observer backstepping

Dynamic positioning (DP) systems for ships are usually designed under the assumption that the kinematic equations be linearized about a constant yaw angle such that linear and gain scheduling techniques can be applied. This paper proposes a globally exponentially stable (GES) nonlinear control where this assumption is removed. A nonlinear observer is included in the design such that only position measurements are required. GES is proven by applying the backstepping design methodology and Lyapunov stability theory. The control law is simulated on two thruster-controlled ships.

On the state observation and output feedback problems for nonlinear uncertain dynamic systems

In this paper, we examine the problems of state observation and state trajectory control by output feedback for the class of non-linear systems in [3,11]. We begin by modifying a known discontinuous variable structure type observer into a continuous type observer that guarantees the observation error is Globally Exponentially Stable (GES). We then modify a known discontinuous variable structure type output feedback controller into continuous type output feedback controller that forces the state to the origin in the GES sense. Specific time-varying bounds on the observation error and the state trajectory are also developed; revealing how the corresponding observer or control parameters can be adjusted to improve the system performance.