Design of dynamical and control systems by the method of inequalities

In the design of dynamical systems, such as automatic regulators and electrical networks, a system is required to satisfy constraints and specifications, which can be represented by a set of simultaneous algebraic inequalities. It is shown how typical design problems lead naturally to the formulation of a set of inequalities, any solution of which characterises an acceptable system. A numerical process for obtaining a solution of a system of inequalities is developed. Applications of the method of inequalities to the design of automatic control systems are discussed. Specific control problems, in single-variable and multivariable systems, are considered, and designs, obtained by the method of inequalities, are compared with those obtained by standard methods of Nyquist, root locus and optimisation.