In this note we present both necessary and sufficient conditions for the existence of a linear static state feedback controller if the system is described by an index one descriptor system. A priori no definiteness restrictions are made w.r.t. the quadratic performance criterium. It is shown...

In this note we consider the question under which conditions all entries of the matrix I-(I+X)-1 are nonnegative in case matrix X is a real positive definite matrix.Sufficient conditions are presented as well as some necessary conditions.One sufficient condition is that matrix X-1 is an inverse...

The aim of the present study is to construct a state feedback controller for a given linear system that minimizes the worst-case effect of an L2 -bounded disturbance. Our setting is different from the usual framework of H -theory in that we consider nonzero initial conditions. The situation is...

In this note we consider the cooperative linear quadratic control problem. That is, the problem where a number of players, all facing a (different) linear quadratic control problem, decide to cooperate in order to optimize their performance. It is well-known, in case the performance criteria are...

In this paper we consider the discounted linear quadratic differential game for descriptor systems that have an index larger than one. We derive both necessary and sufficient conditions for existence of an open-loop Nash (OLN) equilibrium. In a small macro-economic stabilization game we...

Abstract: In this note we generalize a numerical algorithm presented in [9] to calculate all solutions of the scalar algebraic Riccati equations that play an important role in finding feedback Nash equilibria of the scalar N-player linear affine-quadratic differential game. The algorithm is...

In this paper we provide a numerical algorithm to calculate all soft-constrained Nash equilibria in a regular scalar indefinite linear-quadratic game.The algorithm is based on the calculation of the eigenstructure of a certain matrix.The analysis follows the lines of the approach taken by...

Abstract: In this note we sketch a dynamic framework within which the discussion on the macro economic effects of climate change take place. The problem setting is characterized by scientific uncertainties about the development of climate, potential large economic losses and human beings having...