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The problem of the delay-dependent stability of linear systems with multiple time delays is discussed. A new method is first presented for a system with two time delays, in which free weighting matrices are used to express the relationships among the terms of the Leibniz–Newton formula. Next, this method is used to show the equivalence between a system with two identical time delays and a system with a single time delay. Then, a numerical example verifies that the criterion given is effective and is a significant improvement over the existing ones. Finally, the basic idea is extended to a system with multiple time delays. [ABSTRACT FROM AUTHOR]

The problem of sampled-data state reconstruction in linear time invariant systems is considered. A new full order observer structure that can generate intersample state estimation is introduced. The observer synthesis is carried out using the H∞ framework and is shown to have some important advantages over the classical lifting technique that has been used to study similar problems. A simulation example illustrates the application of the proposed design in the fast rate fault detection problem. [ABSTRACT FROM AUTHOR]

The two-dimensional (2-D) system theory iterative learning control (ILC) techniques for linear time-invariant discrete systems are extended to the cases of linear time-variant discrete systems. By exploiting the convergent property of 2-D linear time-variant discrete systems with only one independent variable, a kind of 2-D system theory ILC approach is presented for linear time-variant discrete systems. Sufficient conditions are given for convergence of the proposed ILC rules. Two numerical examples are used to validate the ILC procedures. [ABSTRACT FROM AUTHOR]

A computationally efficient linear matrix inequality (LMI)-based criterion for the global asymptotic stability of discrete-time systems in a state-space realisation with state saturation nonlinearities is presented. The criterion turns out to be an improved generalised version of a previously reported LMI-based criterion. The extension of the approach to a situation involving partial state saturation nonlinearities is performed. [ABSTRACT FROM AUTHOR]

The optimal updating law of the problem of optimal higher-order iterative learning control is given explicitly and the convergence of the tracking errors is proved. Two examples show that the convergence of the optimal higher-order iterative learning control is faster than that of the optimal one-order iterative learning control. [ABSTRACT FROM AUTHOR]

A method of designing linear parameter varying (LPV) control systems based on the parameterisation of all quadratically stabilising controllers is presented. Conceptions of doubly coprime factorisation and Youla parameterisation of LTI systems are extended to LPV systems with respect to quadratic stability using a state space expression. The parameterisation of closed loop systems, which are affine with any quadratically stable Q-parameter, is then described. This description enables the application of the Q-parameter approach to a variety of LPV control system designs. Above all, a systematic H∞ strategy is focused on and a necessary and sufficient condition and also a design scheme of Q to obtain L2-gain performance, are clarified. [ABSTRACT FROM AUTHOR]

The design of a minimum variance regulator for systems operating in dynamical uncertain environments is considered. For minimum variance self-tuning control of an unknown linear time-invariant system, a stable control strategy is developed that improves the transient response by using multiple models to describe the different environments and switching between the relative controllers. The controller is determined at every time instant by the model which best approximates the plant. The performance of the controller is evaluated by a set of simulation tests. [ABSTRACT FROM AUTHOR]

The design of a repetitive control system for linear systems with time-varying norm-bounded uncertainties is presented. Using a Lyapunov functional for the time-delay systems, a sufficient condition is derived in terms of either an algebraic Ricatti inequality or a linear matrix inequality (LMI), which ensures robust stability of the repetitive control system. Based on the derived condition, we show that the repetitive controller design problem can be reformulated as an optimisation problem with an LMI constraint of the free parameter. [ABSTRACT FROM AUTHOR]

Lower and upper bounds are given to calculate the smallest possible left-half-plane where all poles of a single-input single-output plant with no zeros can be stabilised using constant gain feedback. The results are expected to have immediate application areas in control system theory and filter design. [ABSTRACT FROM AUTHOR]