This book develops a nonstandard approach to control systems analysis and design, exploring the properties of a new type of model called non-recursive behavioural models, unlike the recursive behavioural models of classical state space representation. For a real plant exhibiting a linear behaviour in the vicinity of any operating point, a non-recursive behavioural model (associated with an operating point) is defined as a coherent collection of appropriately selected input-state transfers, where, for a given timeline, the plant is actuated by piecewise constant input vectors. This work successively presents: mathematical preliminaries, definitions of linear non-recursive behavioural models, techniques for state controllability analysis, procedures for feedback control and optimal control design. All theoretical results are illustrated by laboratory experiments. This monograph is useful for postgraduate students, research workers and practitioners interested in systems theory and its applications.