Extended Stability Conditions for CDM Controller Design Jo˜ ao Paulo Coelho 1 , J. Boaventura-Cunha 2 and P. B. de Moura Oliveira 2 1 Department of Electrotechnics, School of Technology and Management, Polytechnic Institute of Bragan¸ ca, 5301-857 Bragan¸ ca, Portugal. jpcoelho@ipb.pt 2 INESC TEC - INESC Technology and Science (formerly INESC Porto) and Universidade de Tr´ as-os-Montes e Alto Douro, UTAD, Escola de Ciˆ encias e Tecnologia, Quinta de Prados, 5000-801 Vila Real, Portugal. Abstract. The coefficient diagram method (CDM) is one of the easi- est methods for model based control system design. Its core is based on an algebraic method but it also encompasses a graphical analysis dia- gram that helps the user to evaluate the three main closed-loop system requirements: dynamic behaviour, robustness and stability. This later characteristic is analysed by a set of stability conditions derived from the previous work of Lipatov and Sokolov on sufficient conditions for stability. However, in CDM, only a fraction of the total conditions are considered. This work will show that this fact increases the inconclusive area within the stability space. Moreover an extended set of CDM sta- bility conditions, in conjunction with its graphical interpretation, will be presented. 1 Introduction The coefficient diagram method (CDM) is a mixed algebraic/graphical analysis and synthesis control system design procedure. It was devised by Shunji Manabe during the nineties of the twentieth century [6,7]. Since then, many articles have been published in both CDM theoretical extensions [9, 1] and practical applications [2, 10]. The algebraic component of this method is similar to pole-placement. How- ever, unlike pole-placement, the characteristic polynomial is easily obtained by just defining the predominant time-constant. With the characteristic polyno- mial, and after setting the controller order, the design process comes down to solve a Diophantine type equation. After the algebraic design process is finished, CDM provides a graphical inference tool that can be used to analyse the closed-loop system. This analysis is done regarding three major system properties: bandwidth, robustness and stability. This last attribute is added to the diagram by computing a set of parameters derived from the work of Lipatov and Sokolov in the late sixties [5] and later adapted by Shunji Manabe [8]. In the limit, the Lipatov-Sokolov conditions come down to a set of inequalities involving the coefficients of the characteristic polynomial. Verification, or not,