Reliable H∞ Control for a Class of Switched Nonlinear Systems

Abstract

This paper focuses on the problem of reliable H ∞ control for a class of switched nonlinear systems with actuator failures among a prespecified subset of actuators. In existing works, the reliable H ∞ design methods are all based on a basic assumption that the never failed actuators must stabilize the given system. But when actuators suffer "serious failure"-the never failed actuators can not stabilize the given system, the standard design methods of reliable H ∞ control do not work. Based on the switching technique, the problem can be solved by means of switching among subsystems or finite candidate controllers.Copyright c 2005 IFAC

Controller or actuator failure analysis for systems with time-varying delay

“…Also, the failure controller implies that the complete breakdown of the controller (u = 0) in a certain time interval [6]. Then the system (1) under the controller failure can be Proceedings of the 46th IEEE Conference on Decision and Control New Orleans, LA, USA, Dec. [12][13][14]2007 ThPI27.14 1-4244-1498-9/07/$25.00 ©2007 IEEE. described in the following forṁ…”

“…The "serious failure model " in [13] and [14] is adopted here: once the actuators fails, the un-failed actuators will not stabilize the system. Thus the state of the entire system (1) is dominated by the following piece-wise differential equation:…”

“…Given constants τ > 0, d < 1 and α > 0, if there exist matrices P > 0, Q > 0, R > 0, Z > 0 and W > 0, 46th IEEE CDC, New Orleans, USA, Dec. [12][13][14]2007 ThPI27.14 and matrices N =…”

“…Selecting α * = 0.55 yields T u (t) t ≤ 1 2 according to Cond 1 . Given α = 0.5, T * a = 0.8253 has been obtained according to 46th IEEE CDC, New Orleans, USA, Dec. [12][13][14]2007 ThPI27.14 Cond 2 . Thus, according to (21), if the unavailability rate is not more than 1 2 , that is, the total failure time is not more than half of the whole time, and the failure frequency is less than 1 T * a , then system (29) with actuator or controller failure is still exponentially stable with ||x(t)|| ≤ 2.3772e −0.025t ||x 0 || c1 .…”

Reliable Adaptive Control for Switched Fuzzy Systems

“…In order to investigate the reliable control problem, we classify actuators of i -th switched subsystem (3) into two groups (Wang, Zhao, and Dimirovski, 2005). One is a set of actuators susceptible to failures, denoted by…”