Stabilization over power-constrained parallel Gaussian channels

This technical note is concerned with state-feedback stabilization of multi-input systems over parallel Gaussian channels subject to a total power constraint. Both continuous-time and discrete-time systems are treated under the framework of H2 control, and necessary/sufficient conditions for stabilizability are established in terms of inequalities involving unstable plant poles, transmitted power, and noise variances. These results are further used to clarify the relationship between channel capacity and stabilizability. Compared to single-input systems, a range of technical issues arise. In particular, in the multi-input case, the optimal controller has a separation structure, and the lower bound on channel capacity for some discrete-time systems is unachievable by linear time-invariant (LTI) encoders/decoder

Integral control of port-Hamiltonian systems: non-passive outputs without coordinate transformation

In this paper we present a method for the addition of integral action to non-passive outputs of a class of port-Hamiltonian systems. The proposed integral controller is a dynamic extension, constructed from the open loop system, such that the closed loop preserves the port-Hamiltonian form. It is shown that the controller is able to reject the effects of both matched and unmatched disturbances, preserving the regulation of the non-passive outputs. Previous solutions to this problem have relied on a change of coordinates whereas the presented solution is developed using the original state vector and, therefore, retains its physical interpretation. In addition, the resulting closed loop dynamics have a natural interpretation as a Control by Interconnection scheme.Comment: 8 pages, 2 figure

Large-signal stability conditions for semi-quasi-Z-source inverters: switched and averaged models

The recently introduced semi-quasi-Z-source in- verter can be interpreted as a DC-DC converter whose input- output voltage gain may take any value between minus infinity and 1 depending on the applied duty cycle. In order to generate a sinusoidal voltage waveform at the output of this converter, a time-varying duty cycle needs to be applied. Application of a time-varying duty cycle that produces large-signal behavior requires careful consideration of stability issues. This paper provides stability results for both the large-signal averaged and the switched models of the semi-quasi-Z-source inverter operating in continuous conduction mode. We show that if the load is linear and purely resistive then the boundedness and ultimate boundedness of the state trajectories is guaranteed provided some reasonable operation conditions are ensured. These conditions amount to keeping the duty cycle away from the extreme values 0 or 1 (averaged and switched models), and limiting the maximum PWM switching period (switched model). The results obtained can be used to give theoretical justification to the inverter operation strategy recently proposed by Cao et al. in [1].Comment: Submitted to the IEEE Conf. on Decision and Control, Florence, Italy, 201

On Limitations to the achievable path following performance for linear multivariable plants

In this paper, we consider a problem termed “path following”. This differs from the common problem of reference tracking, in that here we can adjust the speed at which we traverse the reference trajectory. We are interested in ascertaining the degree to which we can track a given trajectory, and in characterizing the class of paths for which we can generate an appropriate temporal specification so that the path can be tracked arbitrarily well in an L2 sense.We give various bounds on the achievable performance, as well as tight results in special cases. In addition, we give a numerical procedure based on convex optimization for computing the achievable performance. The results demonstrate that there are situations where arbitrarily good L2 performance may be achieved even though the origin is not in the convex hull of the positive limit set of the path to be followed

On Limitations to the achievable path following performance for linear multivariable plants

In this paper, we consider a problem termed “path following”. This differs from the common problem of reference tracking, in that here we can adjust the speed at which we traverse the reference trajectory. We are interested in ascertaining the degree to which we can track a given trajectory, and in characterizing the class of paths for which we can generate an appropriate temporal specification so that the path can be tracked arbitrarily well in an L2 sense.We give various bounds on the achievable performance, as well as tight results in special cases. In addition, we give a numerical procedure based on convex optimization for computing the achievable performance. The results demonstrate that there are situations where arbitrarily good L2 performance may be achieved even though the origin is not in the convex hull of the positive limit set of the path to be followed

Numerical Sensitivity of Linear Matrix Inequalities Using Shift and Delta Operators

The numerical sensitivity of linear matrix inequalities (LMIs) arising from discrete-time control with short sampling periods is analyzed using shift and delta operators. The delta operator avoids cancellation problems for short sampling periods, and it includes a system scaling proportional to the inverse of the sampling period. The numerical sensitivity of both these mechanisms is investigated analytically, and verified by numerical examples. The conclusion is that the scaling procedure is (somewhat surprisingly) much more essential for shorter sampling periods than avoiding the cancellation problem

On AIMD Congestion Control in Multiple Bottleneck Networks.

We consider a linear algebraic model of the Additive-Increase Multiplicative-Decrease congestion control algorithm and present results on average fairness and convergence for multiple bottleneck networks. Results are presented for networks of both long-lived and short-lived flows