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This paper develops a methodology for designing a control system composed of a linear time-invariant system interconnecting with multiple decoupled time-invariant memoryless nonlinearities. The design problem is to determine parameters of the system such that its outputs and the nonlinearity inputs always remain within prescribed bounds for all exogenous inputs whose magnitude and slope satisfy certain bounding conditions. By using Schauder fixed point theorem, we show that a design associated with a linear system is also a solution of the problem. Based on this, we further develop surrogate design criteria in the form of the inequalities that can readily be solved in practice. Sufficient conditions for the solvability of such inequalities are given for deadzone and saturation. To show the usefulness and the effectiveness of the methodology, a design example of a load frequency control system with time delay is carried out where deadzone and saturation are taken into account. [ABSTRACT FROM AUTHOR]

The evaluation of peak outputs is an essential component of control systems design in which the outputs are required to remain within their prescribed bounds in the presence of all possible inputs. Characterising a possible set with many bounding conditions can reduce conservatism, thereby yielding a better design. However, this gives rise to difficulty in computing the peak outputs using analytical techniques. This article develops a practical method for computing the peak outputs of linear time-invariant systems for a class of possible sets characterised with many bounding conditions on the two- and/or the infinity-norms of the inputs and their slopes. The original infinite-dimensional convex optimisation problem is approximated as a large-scale convex programme defined in a Euclidean space with sparse matrices, which can be solved efficiently in practice. A case study of control design for a building subject to seismic disturbances is reinvestigated, where three bounding conditions are used. The numerical results show that the design so obtained is better than the previous one. [ABSTRACT FROM AUTHOR]

Control systems designed by the principle of matching gives rise to problems of evaluating the peak output. This paper proposes a practical method for computing the peak output of linear time-invariant and non-anticipative systems for a class of possible sets that are characterized with many bounding conditions on the two- and/or the infinity-norms of the inputs and their derivatives. The original infinite-dimensional convex optimization problem is approximated as a large-scale convex programme defined in a Euclidean space, which are associated with sparse matrices and thus can be solved efficiently in practice. The numerical results show that the method performs satisfactorily, and that using a possible set with many bounding conditions can help to reduce the design conservatism and thereby yield a better match. [ABSTRACT FROM AUTHOR]

Long sequences of linear delay differential equations (DDEs) frequently occur in the design of control systems with delays using iterative-numerical methods, such as the method of inequalities. Zakian I MN recursions for DDEs are suitable for solving this class of problems, since they are reliable and provide results to the desired accuracy, economically even if the systems are stiff. This paper investigates the numerical stability property of the I MN recursions with respect to Barwell's concept of P-stability. The result shows that the recursions using full grade I MN approximants are P-stable if, and only if, N−2≤M≤N−1. [ABSTRACT FROM AUTHOR]