Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2013, Special Issue (2012), Article ID 206190, 10 pages.

p-Stability and p-Stabilizability of Stochastic Nonlinear and Bilinear Hybrid Systems under Stabilizing Switching Rules

Ewelina Seroka and Lesław Socha

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Abstract

The problem of pth mean exponential stability and stabilizability of a class of stochastic nonlinear and bilinear hybrid systems with unstable and stable subsystems is considered. Sufficient conditions for the pth mean exponential stability and stabilizability under a feedback control and stabilizing switching rules are derived. A method for the construction of stabilizing switching rules based on the Lyapunov technique and the knowledge of regions of decreasing the Lyapunov functions for subsystems is given. Two cases, including single Lyapunov function and a a single Lyapunov-like function, are discussed. Obtained results are illustrated by examples.

Article information

Source
J. Appl. Math., Volume 2013, Special Issue (2012), Article ID 206190, 10 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394807629

Digital Object Identifier
doi:10.1155/2013/206190

Mathematical Reviews number (MathSciNet)
MR3035168

Zentralblatt MATH identifier
1266.93061

Citation

Seroka, Ewelina; Socha, Lesław. $p$ -Stability and $p$ -Stabilizability of Stochastic Nonlinear and Bilinear Hybrid Systems under Stabilizing Switching Rules. J. Appl. Math. 2013, Special Issue (2012), Article ID 206190, 10 pages. doi:10.1155/2013/206190. https://projecteuclid.org/euclid.jam/1394807629


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