This paper investigates the robust output tracking problem for a class of large-scale linear uncertain systems with interactions and time delays. Time delays exist in both states and controls. Using the Riccati equation, a procedure for determining decentralized linear control laws is presented such that the closed-loop system asymptotically tracks the reference output and rejects any constant but unknown disturbances. The main feature of this approach is that the uncertain systems may contain time delays in both states and controls as well as in interactions between subsystems. A numerical example is included to show the results.

The robust tracking and model following problem of linear uncertain time-delay systems is investigated in this paper. By using the solution of the algebraic Riccati equation, this paper presents a direct approach to the design of robust tracking controllers. The system is controlled to track dynamic inputs generated from a reference model. In the case of matched uncertainties, the proposed controller ensures uniform ultimate boundedness of tracking errors and, furthermore, the bounds can be made arbitrarily small. In the case of mismatched uncertainties, a sufficient condition is presented such that the controller guarantees uniform ultimate boundedness of tracking errors. Compared with existing results, the main feature of the approach proposed in this paper is that it does not require any precompensator even for the non-Hurwitz nominal system and, obviously, it is a direct method. It also employs linear controllers rather than nonlinear ones. Therefore, the designing method is simple for use and the resulting controller is easy to implement. Numerical examples show that this scheme can accommodate larger uncertainties and is likely to produce less conservative results.

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First, the existence conditions on the solutions to the algebraic Riccati equation are reviewed. Then, a strict proof is presented for a necessary and sufficient condition on the existence of a unique optimal positive definite solution to this equation. By using this condition, some untrue results on the design of robust decentralized controllers are corrected.

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