Uniform Global Stability Research Articles

Integral Characterizations of Uniform Asymptotic and Exponential Stability with Applications

We present integral characterizations of uniform asymptotic stability and uniform exponential stability for differential equations and inclusions. These characterizations are used to establish new results on concluding uniform global asymptotic stability when uniform global stability is already known and uniform convergence must be established by additional arguments. In one case we generalize Matrosov's theorem on the use of a differentiable auxiliary function. In another case we draw conclusions from a system related to the original by suitable output injection.

Integral Characterizations of Set UGAS of Differential Inclusions and Applications

We present an integral characterization of uniform asymptotic stability for differential equations and inclusions. This characterization is used to establish new results on concluding uniform global asymptotic stability when uniform global stability is already known and uniform convergence must be established by additional arguments. We show the utility of our result by generalizing Matrosov's Theorem on the use of a differentiable auxiliary function. Also, we present an application to the stability analysis of time-varying systems.

A theorem for UGAS and ULES of (passive) nonautonomous systems: robust control of mechanical systems and ships

AbstractThe main contribution of this paper is a theorem to guarantee uniform global asymptotic stability (UGAS) and uniform local exponential stability (ULES) for a class of nonlinear non‐autonomous systems which includes passive systems. These properties (and a uniform local Lipschitz condition) guarantee robustness of stability while weaker properties, like uniform global stability plus global convergence, do not. Our main result is then used in the tracking control problem of mechanical systems and ships. We use an adaptive backstepping design and prove UGAS of the closed‐loop tracking error system, in particular, we obtain that both the tracking and parameter estimation errors converge uniformly globally to zero. Copyright © 2001 John Wiley & Sons, Ltd.

P+I form laws for combined adaptive control

The Letter presents ‘proportional + integral’ (P+I) adaptive laws for combined adaptive control, using closed-loop estimation errors. The global uniform stability of the overall system is shown by constructing a new Lyapunov function. Simulation results show that the ‘P+I’ form laws yield improved performance.

Global uniform decay rates for the solutions to wave equation with nonlinear boundary conditions

Wave equation with nonlinear boundary conditions of Neumann type is considered. It is shown that the boundary damping produces a uniform global stability of the corresponding solutions.

Combined direct and indirect approach to adaptive control

An approach to adaptive control is introduced using a combination of both direct and indirect methods. On the basis of estimates of the plant parameters and the current values of the control parameters, closed-loop estimation errors epsilon /sub theta /(t) and epsilon /sub k/(t) are defined. These in turn are used in the adaptive laws for updating both identification and control parameters. The global uniform stability of the overall system is shown by constructing a Lyapunov function. Only the control of a first-order plant is treated in detail, to get across the principal concepts involved. In particular, the dynamic adjustment of the control parameters based on the estimates of the plant parameters is introduced as an indirect method and is the precursor of the combined method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>