Joan Peuteman

A new asymptotic stability criterion for nonlinear time-variant differential equations

A new sufficient condition for asymptotic stability of ordinary differential equations is proposed. Unlike classical Lyapunov theory, the time derivative along solutions of the Lyapunov function may have positive and negative values. The classical Lyapunov approach may be regarded as an infinitesimal version of the present theorem. Verification in practical problems is harder than in the classical case; an example is included in order to indicate how the present theorem may be applied.

Averaging techniques without requiring a fast time-varying differential equation

An averaging result is presented for local uniform asymptotic stability of nonlinear differential equations without requiring a fast time-varying vectorfield. The nonlinearity plays a crucial role: close to the origin, the trajectories vary slowly compared to the time dependence of the vectorfield. The result generalises averaging results which prove stability properties for systems having a homogeneous vectorfield with positive order. The result is illustrated with several examples.

New criteria for exponential and uniform asymptotic stability of nonlinear time-variant differential equations

Within the Lyapunov framework, sufficient conditions for exponential and uniform asymptotic stability of ordinary differential equations are proposed. Unlike with classical Lyapunov theory, the time derivative of the Lyapunov function, taken along solutions of the system, may have positive and negative values. Verification of the conditions of the main theorems may be harder than in the classical case. It is shown that the proposed conditions are useful for the investigation of the exponential stability of fast time-varying systems. This sets the stability study by means of averaging in a Lyapunov context. In particular, it is established that exponential stability of the averaged system implies exponential stability of the original fast time-varying system.

General equations for the characteristic impedance matrix and termination network of multiconductor transmission lines

To avoid reflections on a multiconductor transmission line, the transmission line must be terminated by its characteristic impedance matrix [Zc]. In this paper, [Zc] and the impedance matching network is calculated for the lossy (n+1)- conductor transmission line. The result is an easy-to-use equation, making time consuming matrix calculations unnecessary.

A Vector Impedance Meter Method to Characterize Multiconductor Transmission-Line Parameters

For analyzing and simulating the behavior of multiconductor transmission lines, a measurement of the transmission-line parameters is needed. In this paper, an accurate method for measuring the full capacitance, inductance, resistance, and shunt-resistance matrices by a vector impedance meter is described. The method has been applied for frequencies in a range from 20 kHz up to 30 MHz.

An analytical calculation of the behavior of a line termination network

When feeding an induction motor by a PWM-inverter through long cables, reflections occur and overvoltages may arise. Using a terminator in parallel with the motor, the overvoltages are reduced. An analytical calculation of the motor voltage is obtained using transmission line theory. Simulations and measurements allow to verify the results.