The least-squares transformation of a discrete-time multivariable linear system into a desired one by convolving the first with-a polynomial system yields optimal polynomial solutions to the problems of system compensation, inversion and approximation. The polynomial coefficients are obtained from the solution to a so-called normal linear matrix equation, whose coefficients are shown to be the ...

1. Explain why difference equations result from digital control of analog systems. 2. Obtain the z-transform of a given time sequence and the time sequence corresponding to a function of z. 3. Solve linear time-invariant (LTI) difference equations using the z-transform. 4. Obtain the z-transfer function of an LTI system. 5. Obtain the time response of an LTI system using its transfer function o...

What follows is a quick survey of the main ingredients in the theory of discrete-time Markov processes. It is a birds' view, rather than the deenitive \state of the art." To maximize accessibility, the nomenclature of mathematical probability is avoided, although rigor is not sacriiced. To compensate, examples (and counterexamples) abound and the bibliography is annotated. Relevance to control ...

This paper focuses on the fundamentals of discrete-time models using recursive utility. We examine the relation between preferences, utility, and aggregator, the existence of optimal paths, and several notions of impatience. In the one-sector model, we characterize optimal paths and derive a turnpike theorem. Topics beyond the scope of this paper include continuous time recursive utility, model...

The original continuous-time “goldfish” dynamical system is characterized by two neat formulas, the first of which provides the N Newtonian equations of motion of this dynamical system, while the second provides the solution of the corresponding initial-value problem. Several other, more general, solvable dynamical systems “of goldfish type” have been identified over time, featuring, in the rig...

In this section we study the relation between throughput and queue-length distributions in discrete-time closed cyclic networks when the number of customers and the number of nodes grows unboundedly. To state our findings more precisely: For each positive integer N , consider a cyclic network with n(N) nodes and k(N) customers. We suppose that there are only finitely many types of nodes. That i...

of its members. The process of these macro-individuals has independently reproducing elements, as different sibships are independent of each other. The numbers of “macro children” need, however, not be distributed identically (e.g., we might expect a large sibship to give birth to more children than a small one). Thus the macro-process is a multi-type branching process, and in the Galton–Watson...

Techniques for developing low-complexity, robust Digital Signal Processing (DSP) algorithms with low-power consumption have become increasingly important. This thesis explores a framework, discrete-time randomized sampling, which allows the design of algorithms that meet some desired complexity, robustness or power constraints. Three distinct sampling schemes are presented based on randomized s...