Mathematical control of complex systems

Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Stabilization of positive switched systems with time-varying delays under asynchronous switching

This paper investigates the state feedback stabilization problem for a class of positive switched systems with time-varying delays under asynchronous switching in the frameworks of continuous-time and discrete-time dynamics. The so-called asynchronous switching means that the switches between the candidate controllers and system modes are asynchronous. By constructing an appropriate co-positive type Lyapunov-Krasovskii functional and further allowing the functional to increase during the running time of active subsystems, sufficient conditions are provided to guarantee the exponential stability of the resulting closed-loop systems, and the corresponding controller gain matrices and admissible switching signals are presented. Finally, two illustrative examples are given to show the effectiveness of the proposed methods

Robust Fault Detection of Switched Linear Systems with State Delays

This correspondence deals with the problem of robust fault detection for discrete-time switched systems with state delays under an arbitrary switching signal. The fault detection filter is used as the residual generator, in which the filter parameters are dependent on the system mode. Attention is focused on designing the robust fault detection filter such that, for unknown inputs, control inputs, and model uncertainties, the estimation error between the residuals and faults is minimized. The problem of robust fault detection is converted into an H infin-filtering problem. By a switched Lyapunov functional approach, a sufficient condition for the solvability of this problem is established in terms of linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of the proposed method

Analysis and synthesis of randomly switched systems with known sojourn probabilities

In this paper, a new approach is proposed and investigated for the stability analysis and stabilizing controller design of randomly switched linear discrete systems. The approach is based on sojourn probabilities and it is assumed that these probabilities are known a prior. A new Lyapunov functional is constructed and two main theorems are proved in this paper. Theorem 1 gives a sufficient condition for a switched system with known sojourn probabilities to be mean square stable. Theorem 2 gives a sufficient condition for the design of a stabilizing controller. The applications of these theorems and the corresponding corollary and lemma are demonstrated by three numerical examples. Finally, some future research is proposed