Input-to-State Stability and H ∞ Performance for Stochastic Control Systems with Piece wise Constant Arguments

Mohamad S. Alwan () and Xinzhi Liu ()
Additional contact information
Mohamad S. Alwan: University of Waterloo, Department of Applied Mathematics
Xinzhi Liu: University of Waterloo, Department of Applied Mathematics

A chapter in Mathematical and Computational Approaches in Advancing Modern Science and Engineering, 2016, pp 367-377 from Springer

Abstract: Abstract This paper addresses stochastic control system of differential equations with piecewise constant arguments (SEPCA SEPCA ). The piecewise constant arguments are of delay type. The system is viewed as a hybrid Hybrid system (or particularly switched) system Switched systems . This approach motivates the applicability of the classical theory of ordinary differential equations, but not of functional differential equations, and the design of a switching law. The main theme of this work is to establish the problems of input-to-state stabilization (ISS ISS ), and H ∞ H ∞ performance for a class of an uncertain control SEPCA. To analyze these result, a common Lyapunov function Lyapunov function together with the techniques of differential inequalities and Razumikhin Razumikhin condition is used. A numerical example with simulations is presented to clarify the validity of the proposed theoretical approaches.

Keywords: Lyapunov Function; Exponential Stability; Functional Differential Equation; Piecewise Constant Function; Brownian Motion Process (search for similar items in EconPapers)
Date: 2016
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-30379-6_34

Ordering information: This item can be ordered from
http://www.springer.com/9783319303796

DOI: 10.1007/978-3-319-30379-6_34

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().