H∞ Optimal Controller Design With Closed-Loop Positive Real Constraints

Positive real constraints on the closed-loop of linear systems guarantee stable interaction with arbitrary passive environments. Two such methods of H∞ optimal controller synthesis subject to a positive real constraint are presented and demonstrated on numerical examples. The first approach is based on an established multi-objective optimal control framework using linear matrix inequalities and is shown to be overly restrictive and ultimately infeasible. The second method employs a sector transformation to substitute the positive real constraint with an equivalent H∞ constraint. In two examples, this method is shown to be more reliable and displays little change in the achieved H∞ norm compared to the unconstrained design, making it a promising tool for passivity-based controller design.

Placing Future Senate Reform in Context

As the opening speaker at the Centre for Constitutional Studies’ March 2015 conference entitled “Time for Boldness on Senate Reform,” I took it as my mission not to advance any bold ideas of my own (though some found my comments on Senate numbers particularly bold). Rather, I tried to set the context for other participants’ bold ideas. This paper follows a format similar to my talk. In the first part, I explain the current state of scholarly knowledge of second chambers and bicameralism. In the second part, I discuss the accepted orthodoxy that exists in Canada concerning Senate reform, namely that it must simultaneously address the method of selection, the numbers of seats each province gets, and the powers of the Senate. In the third part, I discuss the real constraint on Senate reform which is sociological and not constitutional. I left it to my fellow panelists to explore the Supreme Court ruling in the reference on Senate reform.

Economic Policy Uncertainty and Small Business Expansion

Small businesses continue to report problems obtaining the financing they need. Because small business owners may rely heavily on the value of their homes to finance their businesses (through mortgages or home equity lines), the fall in housing prices might be one of the causes of their difficulty. We analyze information from a variety of sources and find that homes do constitute a significant source of capital for small business owners and that the impact of the recent decline in housing prices is significant enough to be a real constraint on small business finances.

Repugnance as a Constraint on Markets

This essay examines how repugnance sometimes constrains what transactions and markets we see. When my colleagues and I have helped design markets and allocation procedures, we have often found that distaste for certain kinds of transactions is a real constraint, every bit as real as the constraints imposed by technology or by the requirements of incentives and efficiency. I'll first consider a range of examples, from slavery and indentured servitude (which are much more repugnant now than they once were) to lending money for interest (which used to be widely repugnant but no longer is), and from bans on eating horse meat in California to bans on dwarf tossing in France. An example of special interest will be the widespread laws against the buying and selling of organs for transplantation. The historical record suggests that while repugnance can change over time, it can persist for a very long time, although changes in institutions that reflect repugnance can occur relatively quickly when the underlying repugnance changes.