Minimal stabilization is considered for a scalar system. The minimal stabilization problem is shown to be equivalent to the problem of intersecting the space of stable polynomials with a linear manifold. It is proved that the linear manifold can be described by a linear system of algebraic equations with Hankel structure. The article provides examples of some applications of the minimal stabilizer search algorithm.

The article presents an approach to simultaneous stabilization of a finite family of linear dynamical plants. Two main issues are considered: finding the existence conditions for a single controller and an algorithm to construct such a controller if it exists. The approach proposed in this article is based on the properties of affine transformations of the controller parameter space into the coefficient space of characteristic polynomials of the stabilized plants. A general scheme is presented for analyzing simultaneous stabilizability of finite families of plants and a numerical algorithm is investigated to find a stabilizing controller by the interval analysis method.

In this paper, we consider some scheduling problems on a single machine, where weighted or unweighted total tardiness has to be maximized in contrast to usual minimization problems. These problems are theoretically important and have also practical interpretations. For the weighted tardiness maximization problem, we present an NP-hardness proof and a pseudo-polynomial solution algorithm. For the unweighted total tardiness maximization problem with release dates, NP-hardness is proven. Complexity results for some other classical objective functions (e.g., the number of tardy jobs, total completion time) and various additional constraints (e.g., deadlines, weights and/or release dates of jobs may be given) are presented as well.

Mechanism Design (MD) is a branch of game theory which deals with conflict situations involving a principal and a set of active agents (usually in the presence of asymmetric information). Mechanism design theory delivers a solution to many management problems in the form of a control mechanism, (i.e., a formalized routine of decision-making). Formal results of MD can change the fundamentals of managerial practice by introducing decision-making mechanisms in organizations, which are efficient and robust with respect to employees’ self-serving behaviour. The proposed book seeks a more intensive application of MD methodology and its formal results in organizations. The main aim of the book is to provide readers with the basics of an MD-based view on managerial problems, so that intra-firm policies can be analysed through the looking glass of employees’ behavioural response. A systematic introduction of the underlying MD methodology is combined with a collection of ready-to-use mechanisms for solving typical management problems. The use of MD by individual managers is facilitated by bringing together mathematical and business literature in a single treatise. This book is not a purely academic monograph as it contains as few formulas as possible, and no formal proofs (references to formal results are provided throughout the text). Courses on MD for managers are not common in business schools now, and our book represents the perfect material for such a course. (Imprint: Nova)