Abstract
This paper is concerned with the reachable set estimation problem for neutral Markovian jump systems with bounded peak disturbances, which was rarely proposed for neutral Markovian jump systems. The main consideration is to find a proper method to obtain the no-ellipsoidal bound of the reachable set for neutral Markovian jump system as small as possible. By applying Lyapunov functional method, some derived conditions are obtained in the form of matrix inequalities. Finally, numerical examples are presented to demonstrate the effectiveness of the theoretical results.
Highlights
In practice and engineering applications, many dynamical systems may cause abrupt variations in their structure, due to stochastic failures or repairs of the components, changes in the interconnections of subsystems, sudden environment changes, and so on
This paper is concerned with the reachable set estimation problem for neutral Markovian jump systems with bounded peak disturbances, which was rarely proposed for neutral Markovian jump systems
The main consideration is to find a proper method to obtain the no-ellipsoidal bound of the reachable set for neutral Markovian jump system as small as possible
Summary
In practice and engineering applications, many dynamical systems may cause abrupt variations in their structure, due to stochastic failures or repairs of the components, changes in the interconnections of subsystems, sudden environment changes, and so on. If the value of the derivative of the time delay is large, this method will yield a bigger ellipsoid bounding the reachable set than that in [16]. The bound of reachable sets for neutral Markovian jump systems with bounded peak disturbances has not been investigated, which motivates this paper. We consider the problem of finding the no-ellipsoidal bound of reachable sets for neutral Markovian jump systems with bounded peak disturbances. Based on the modified Lyapunov-Krasovskii type functional, some delay-dependent results are derived in the form of matrix inequalities containing only one non-convex scalar. A modified matrix inequality is used to remove the limitation on the variation rate of the delay and obtain a “smaller” no-ellipsoidal bound of reachable sets. Numerical examples illustrate the effectiveness and improvement of the obtained results
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