A Bode Sensitivity Integral for Linear Time-Periodic Systems

Bode's sensitivity integral is a well-known formula that quantifies some of the limitations in feedback control for linear time-invariant systems. In this note, we show that there is a similar formula for linear time-periodic systems. The harmonic transfer function is used to prove the result. We use the notion of roll-off 2, which means that the first time-varying Markov parameter is equal to zero. It then follows that the harmonic transfer function is an analytic operator and a trace class operator. These facts are used to prove the result

Optimal Control over Networks with Long Random Delays

This paper studies the effects of stochastic time delays on automatic control systems which uses communication networks. We assume a linear process to be controlled and known delay probability distributions.The contribution of this paper is to extend the theory in(Nilsson 1998) to delays that may be longer than one sample period.Using a quadratic cost we find the optimal full-state-information controller. We also show that the standard Kalman filter is an optimal observer, and that the separation principle holds

Using a Gaussian Channel Twice

The problem of communicating one bit over a memoryless Gaussian channel with an energy constraint is discussed. It is assumed that the channel is allowed to be used only two times. An ideal feedback channel is also supposed available. The optimal feedback strategy and the bit-error probability are derived. It is shown that feedback gives a significant performance gain and that the optimal strategy is discontinuous. It is also shown that most of the performance increase can be obtained even with a one-bit feedback channel

Frequency-Domain Analysis of Linear Time-Periodic Systems

In this paper, we study convergence of truncated representations of the frequency-response operator of a linear time-periodic system. The frequency-response operator is frequently called the harmonic transfer function. We introduce the concepts of input, output, and skew roll-off. These concepts are related to the decay rates of elements in the harmonic transfer function. A system with high input and output roll-off may be well approximated by a low-dimensional matrix function. A system with high skew roll-off may be represented by an operator with only few diagonals. Furthermore, the roll-off rates are shown to be determined by certain properties of Taylor and Fourier expansions of the periodic systems. Finally, we clarify the connections between the different methods for computing the harmonic transfer function that are suggested in the literature

Topics in Digital and Robust Control of Linear Systems

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LQG Control Over a Markov Communication Network

We formulate and solve a control problem where data are sent over a communication network that introduces random time delays. Past time delays are assumed known by the use of timestamps and the probability distribution of future delays are modeled with a Markov chain with continuous observation densities. We generalize previous results on LQG control of jump linear systems to cover this situation