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Robust Non-fragile Controllers Design
for Uncertain Linear Switched Systems
Junyong Zhai , Bin Wang, and Shumin Fei
Key Laboratory of Measurement and Control of CSE, Ministry of Education
Southeast University, Nanjing 210096, China
jyzhai@seu.edu.cn
http://www.springer.com/lncs
Abstract. This paper deals with the problem of how to design ro-
bust non-fragile controllers for linear switched systems with uncertainties
which are included in both the system matrix and the input one. Combin-
ing the piecewise Lyapunov function with the average dwell-time method,
we develop the sucient conditions for the existence of non-fragile state
feedback controllers, which guarantee that the switched system is ex-
ponentially stable and has a certain stability margin for all admissible
uncertainties by means of switching among multiple models. The corre-
sponding results are given in terms of linear matrix inequalities.
Keywords: Non-fragile, piecewise Lyapunov functions, average dwell-
time, exponentially stable.
1 Introduction
A hybrid dynamical system consists of a family of continuous-time subsystems
and a rule that orchestrates the switching between them. Due to their significance
both in theory development and in practical applications, switched systems have
been attracting considerable attention during the last decades [1-8]. Switched
systems have numerous applications in control of mechanical systems, the auto-
motive industry, aircraft and air trac control, switching power converters, and
many other fields. Hybrid control, which is based on switching between different
models and controllers, has also received growing interest, due to its advantages,
for instance, on achieving stability, improving transient response, and provid-
ing an effective mechanism to cope with highly complex systems and systems
with large uncertainties. Two key problems in the study of switched systems
are the stability analysis and control synthesis. It has been shown that average
dwell- time approach is an effective tool for choosing certain switching laws, un-
der which asymptotic and/or exponential stability can be obtained [9-11]. For
the analysis of stability of the switched systems, there are mainly about com-
mon Lyapunov function, multiple Lyapunov functions and dwell-time method.
In [12-15] have designed the controllers with appropriate switched rules using
 
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