L(infinity) optimal control of SISO continuous-time systems

In this paper we study the problem of designing a controller that minimizes the weighted amplitude of the time response due to a given, fixed input signal for SISO continuous-time systems. The main result of the paper shows that this problem admits a minimizing solution in L(infinity) and that the optimal closed-loop system has a special structure: a sum of delayed step functions, all having the same amplitude. Thus the optimal controller has a non-rational transfer function. Although in the general case finding this controller entails solving an infinite-dimensional linear-programming problem, we show that in some special cases the optimal solutions have closed-form expressions and can be found by solving a set of algebraic equations. Finally, we address the issue of selecting time and frequency domain weighting functions. This paper together with our paper 'Rational L(infinity)-suboptimal controller for SISO continuous time systems' (IEEE Trans. Autom. Control, AC-41, 1358-1363 (1996)), which deals with the design of rational L(infinity), suboptimal controllers for general Systems, give a complete solution of the L(infinity) control problem. (C) 1997 Elsevier Science Ltd.