Systems With Delays Decentralized Robust H_ ¡Þ Control And Filtering

Decentralized control is an important branch of large-scale system theory because of its reliability, economy, flexibility and so on. With the successful application of linear matrix inequality (LMI) to the research of robust control, many inner and oversea scholars intend to transform the robust stability and robust performance of uncertain systems into solving the problems of LMI. The problems of robust control and filtering for several classes of uncertain time-delay large-scale systems are studied in this paper. The major contributions of this paper are shown as follows:(1) The robust decentralized H_∞control problems of uncertain multi-channel time-delay systems are considered both for continue-time case and discrete-time case. The uncertainties are assumed to be time-invariant, norm-bounded, and exist in the system, time-delay and control input matrices. The sufficient condition for the uncertain multi-channel time-delay continue and discrete system to be robustly stabilizable with a specified disturbance attenuation level are derived based on the bounded real lemma of time-delay systems, which is reduced to a feasibility problem of a nonlinear matrix inequality (NMI). A two-stage homotopy method is employed to solve the NMI iteratively. First, a decentralized controller for the nominal time-delay system with no uncertainty is computed by imposing structural constraints on the coefficient matrices of the controller gradually. Then, the decentralized controller is modified, again gradually, to cope with the uncertainties. On each stage, a variable is fixed alternately at the iterations to reduce the NMI to a linear matrix inequality. The output feedback controller is obtained by solving linear matrix inequalities.(2) Decentralized robust H_∞, control problem for uncertain multichannel time-delay continue and discrete systems are investigated. The sufficient condition for the uncertain multi-channel time-delay system to be robustly stabilizable with a specified disturbance attentation level are derived based on the theorem of Lyapunov stability theory by setting the Lyapunov matrix as block diagonal appropriately according to the desired order of the controller, which is reduced to a feasibility problem of a linear matrix inequality directly.(3) Delay dependant decentralized H_∞filtering for a class of uncertain interconnected systems is considered where the uncertainties are assumed to satisfy the norm-bounded conditions. First, combining the Lyapunov-Krasovskii functional approach and the delay integral inequality of matrices, a sufficient condition of the existence of the robust decentralized H_∞, filter is derived which makes the error systems asymptotically stable and satisfies the H_∞, norm of the transfer function from noise input to error output less than the specified up-bound on the basis of the form of uncertainties. Then, the above sufficient condition is transformed to a system of easily solvable LMIs via a series of equivalent transformation. Based on the LMI toolbox of Matlab software, these LMIs can be directly solved.