Search

This paper investigates gain-scheduled control design for linear systems with time-varying state delays subject to actuator saturation and external disturbance. Assuming the disturbance is peak bounded, a sufficient delay-dependent condition is established to guarantee that a family of level sets, corresponding to a novel parameter-dependent Lyapunov–Krasovskii functional, are nested and invariant to the closed-loop system. The invariant sets are then used to obtain nested reachable sets (ellipsoids) to bound the closed-loop states. A family of continuous controllers are designed based on these nested ellipsoids. The controller with the best performance is selected, each time, based on the closed-loop state vector, while complying with the saturation bound, and the resulting closed-loop system is locally input-to-state stable. All conditions are represented in the form of linear matrix inequalities (LMIs) by the linear spline method. Finally, the benefit of the control method is illustrated by two examples. [ABSTRACT FROM AUTHOR]

We discuss a variation of dilated matrix inequalities for the conventional Bounded Real matrix inequality and other similarly structured inequalities. Here, system matrices are separated from Lyapunov matrix to allow the use of different Lyapunov matrices in multi-objective and robust problems. The search involves a bounded scalar parameter that enters the problem nonlinearly and is dealt with a line search. To demonstrate the benefits of the new dilated matrix inequalities over the conventional ones, an example of controller synthesis with ℒ2-gain performance measure (ℋ∞ control) for a system with polytopic uncertainty (robust problem) has been studied. It is shown that for the resulting robust problem the performance obtained via the dilated form is at least equal to that of the conventional one. Also, the connection between the proposed dilated form and the Full Block S-procedure is discussed. [ABSTRACT FROM AUTHOR]