Fast Time-varying Research Articles

Averaging Results for Homogeneous Differential Equations

Within the Liapunov framework, a sufficient condition for uniform asymptotic stability of ordinary differential equations is proposed. Unlike with classical Liapunov theory, the time derivative of the Liapunov function, taken along solutions of the system, may have positive and negative values. It is shown that the proposed condition is useful for the study of uniform asymptotic stability of homogeneous systems with order τ > 0. In particular, it is established that asymptotic stability of the averaged homogeneous system implies local uniform asymptotic stability of the original time-varying homogeneous system. This shows that averaging techniques may play a prominent role in the study of homogeneous —not necessarily fast timevarying— systems. Semiglobal stability results may be obtained by 'speeding up' the system by means of a change of time-scale.

ROBUST CONTROL DESIGN FOR A CLASS OF MISMATCHED COUPLED UNCERTAIN SYSTEMS

We consider a control design problem for a class of mismatched uncertain systems. The uncertainty is (possibly fast) time-varying. A new way of characterizing the structure of uncertainty is submitted. A class of robust controls, which is based on the possible bound of uncertainty, is proposed. The result shown here renders some previous development in this area as a special case. Illustrative examples include ecological systems, chemical reaction processes, electromechanical systems and heating processes. © 1997 John Wiley & Sons, Ltd.

Decentralized robust control for interconnected nonlinear systems

Decentralized robust control of strongly interconnected uncertain systems is addressed in this paper. The uncertainties we consider here may include parameter uncertainty and input disturbance that may be nonlinear and (possibly fast) time-varying. We show specially how both internal and external uncertainties are taken into considerations. This work covers a broad class of large-scale systems since the current consideration renders all previous settings as special cases. Stability analysis with the proposed controllers is provided.

Decentralized robust control design for uncertain delay systems

We consider a class of large-scale uncertain delay systems. The uncertain parameter vector in the system is possibly fast time-varying. It may be nonlinear in the system dynamics. No statistical or fuzzy information of the uncertainty is known. Based on only the possible bound of the uncertain parameter, a decentralized linear robust control is proposed, which renders the system asymptotically stable.

Robust control design for a class of mismatched uncertain nonlinear systems

We consider the robust control design problem for a class of nonlinear uncertain systems. The uncertainty in the system may be due to parameter variations and/or nonlinearity. It may be (possibly fast) time-varying. The system does not satisfy the so-called matching condition. Under a state transformation, which is based on the possible bound of the uncertainty, a robust control scheme can be designed. The control renders the uncertain system practically stable. Furthermore, the uniform ultimate boundedness ball and uniform stability ball can be made arbitrarily small by suitable choice of design parameters.

An adaptive variable structure control for a class of nonlinear systems

Motivated by the recent advance in adaptive output-feedback control for a class of nonlinear systems which can be transformed into the so-called output-feedback form [7,10,11], an adaptive structure controller is proposed in this paper to solve the nonlinear model reference adaptive control problem. It is shown that an asymptotic output tracking performance can be achieved for this class of nonlinear system even if some nonlinearity is not available or some unknown parameters are fast time-varying.