Design of performance robustness for uncertain linear systems with state and control delays

Abstract

TABLE I RELIABLE CONTROLLER DESIGN RESULTSSimilarly, by solving the ARE's in (42) and (43) in Corollaries 3.7, we have an output feedback controller 6 s of the form (4) and (5) Both of these two controllers 6 a and 6 s can provide internal stability and guaranteed disturbance attenuation for the closed-loop system not only when both control channels are operational but also when any of these two control channels experiences an outage.The design results are given in Table I. The two values of the closed-loop disturbance attenuation are computed for each of the two controllers. Namely:o: when there is no outage; c : when there is a controller failure.The "Design " in Table I is the value of used in solving the two corresponding design equations.The actual achievable values of (namely o and c) for the closed-loop system are all less than and quite close to the value of for which the design equations have solutions and the conditions in the Corollaries are satisfied. This indicates that degree of conservativeness in the design method is not very severe.From Table I, it would seem that the actual system performance would be better when some controller failure occurs, contrary to the desirable property of graceful degradation of performance. This is so, however, because a controller failure (modeled as an actuator outage and/or sensor outage) effectively eliminates one column and/or one row of the closed-loop transfer function matrix. This is similar to an observation made in [3]. ACKNOWLEDGMENTThe authors wish to thank the reviewers for many useful suggestions on the initial manuscript of the present work. Syst., vol. 15, no. 6, pp. 37-48, 1995. [11] M. Kinnaert, R. Hanus, and P. Arte, "Fault detection and isolation for unstable linear systems," IEEE Trans. Automat. Contr., vol. 40, pp. 740-742, Apr. 1995. [12] C.-C. Tsui, "A general failure detection, isolation and accommodation system with model uncertainty and measurement noise," IEEE Trans. Automat. Contr., vol. 39, pp. 2318-2321, Nov. 1994. REFERENCES Design of Performance Robustness for Uncertain Linear Systems with State and Control DelaysJ. S. Luo, P. P. J. van den Bosch, S. Weiland, and A. GoldenbergeAbstract-The linear systems considered in this paper are subject to uncertain perturbations of norm-bounded time-varying parameters and multiple time delays in system state and control. The time delays are uncertain, independent of each other, and allowed to be time-varying. The integral quadratic cost criterion is employed to measure system performance. Using solutions of Lyapunov and Riccati equations, a linear state feedback control law is proposed to stabilize the perturbed system and to guarantee an upper bound of system performance, which is applicable to arbitrary time delays.

Adaptive control for a class of nonlinear systems with time-varying delays in state and input

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Robust Control for Uncertain Linear Differential Algebraic Systems with Time Delays

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Robust H∞ control of uncertain nonlinear systems with state and input time-varying delays

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