Recursive Discrete-Time Models for Continuous-Time Systems Under Band-Limited Assumptions

Band-Limited Stochastic Processes in Discrete and Continuous Time

In the theory of stochastic differential equations, it is commonly assumed that the forcing function is a Wiener process. Such a process has an infinite bandwidth in the frequency domain. In practice, however, all stochastic processes have a limited bandwidth. A theory of band-limited linear stochastic processes is described that reflects this reality, and it is shown how the corresponding ARMA...

Optimal Finite-time Control of Positive Linear Discrete-time Systems

This paper considers solving optimization problem for linear discrete time systems such that closed-loop discrete-time system is positive (i.e., all of its state variables have non-negative values) and also finite-time stable. For this purpose, by considering a quadratic cost function, an optimal controller is designed such that in addition to minimizing the cost function, the positivity proper...

A Robust Control Design Technique for Discrete-Time Systems

A robust state feedback design subject to placement of the closed loop eigenvalues in a prescribed region of unit circle is presented. Quantitative measures of robustness and disturbance rejection are investigated. A stochastic optimization algorithm is used to effect trade-off between the free design parameters and to accomplish all the design criteria. A numerical example is given to illustra...

Discrete-time Equivalents to Continuous-time Systems

MCMC for continuous-time discrete-state systems

We propose a simple and novel framework for MCMC inference in continuoustime discrete-state systems with pure jump trajectories. We construct an exact MCMC sampler for such systems by alternately sampling a random discretization of time given a trajectory of the system, and then a new trajectory given the discretization. The first step can be performed efficiently using properties of the Poisso...