Stability of uncertain piecewise affine systems with time delay: delay-dependent Lyapunov approach

This article addresses the problem of robust stability of piecewise affine (PWA) uncertain systems with unknown time-varying delay in the state. It is assumed that the uncertainty is norm bounded and that upper bounds on the state delay and its rate of change are available. A set of linear matrix inequalities (LMIs) is derived providing sufficient conditions for the stability of the system. These conditions depend on the upper bound of the delay. The main contributions of the article are as follows. First, new delay-dependent LMI conditions are derived for the stability of PWA time-delay systems. Second, the stability conditions are extended to the case of uncertain PWA time delay systems. Numerical examples are presented to show the effectiveness of the approach

Stability analysis and controller design for switched time-delay systems

In this thesis, the stability analysis and control synthesis for uncertain switched time-delay systems are investigated. It is known that a wide variety of real-world systems are subject to uncertainty and also time-delay in their dynamics. These characteristics, if not taken into consideration in analysis and synthesis, can lead to important problems such as performance degradation or instability in a control system. On the other hand, the switching phenomenon often appears in numerous applications, where abrupt change is inevitable in the system model. Switching behavior in this type of systems can be triggered either by time, or by the state of the system. A theoretical framework to study various features of switched systems in the presence of uncertainty and time-delay (both neutral and retarded) would be of particular interest in important applications such as network control systems, power systems and communication networks. To address the problem of robust stability for the class of uncertain switched systems with unknown time-varying delay discussed above, sufficient conditions in the form of linear matrix inequalities (LMI) are derived. An adaptive switching control algorithm is then proposed for the stabilization of uncertain discrete time-delay systems subject to disturbance. It is assumed that the discrete time-delay system is highly uncertain, such that a single fixed controller cannot stabilize it effectively. Sufficient conditions are provided subsequently for the stability of switched time-delay systems with polytopic-type uncertainties. Moreover, an adaptive control scheme is provided to stabilize the uncertain neutral time-delay systems when the upper bounds on the system uncertainties are not available a priori . Simulations are provided throughout the thesis to support the theoretical result