This paper presents the solution of output feedback H∞ control problem for linear neutral systems with unknown constant multiple state delays in delay independent case, without any restrictions on plant matrices D12 and D21. First, some sufficient conditions for the solution of this problem are obtained in closed-loop system matrices in both linear matrix inequality (LMI) and algebraic Riccati inequality (ARI) forms, by standard Lyapunov-Krazovskii functional in delay independent multi-delay case. Because of the complexity of the solution of the compensator from these inequalities, equivalent sufficient conditions are derived for designing output feedback controller which stabilizes the closed-loop neutral system under consideration and guarantees an H∞-norm bound constraint on the disturbance attenuation. These conditions are of the form two ARIs and, for simplicity in computation equivalent LMIs are given. Finally, output feedback H∞ controller design is achieved and the results are illustrated in some numerical examples.
In this work, interval time-delay switched systems having completely unstable and mixed stable matrices of the state vector are considered. An observer-based controller is designed for finite-time boundedness and H∞-control of these systems. New sufficient conditions on the existence of a desired observer are developed and new average dwell-time bounds are introduced separately in case of unstable and mixed stable subsystems. An algorithm is presented for the calculation of unknown constants in the average dwell-time bounds which depend on nonlinear matrices in terms of the cone complementarity linearization method. Finally, numerical examples are given for the effectiveness and validity of the proposed solutions.
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