RETRACTED ARTICLE: Boundary behaviors for linear systems of subsolutions of the stationary Schrödinger equation

Zongcai Jiang,Francisco Marco Uso

doi:10.1186/s13660-016-1172-3

Zongcai Jiang, Francisco Marco Uso

Open Access

https://doi.org/10.1186/s13660-016-1172-3

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Abstract

AbstractThis paper investigates the boundary behaviors for linear systems of subsolutions of the stationary Schrödinger equation, which contain unstable subsystems. Our first aim is to establish a state-feedback switching law guaranteeing the continuous-time systems to be uniformly exponentially stable. And then we present sufficient and necessary for the stability of the systems with two Schrödinger subsystems. Finally, an illustrative example is given to verify the result.

Highlights

It is well known that there exists a large class of systems whose states are always nonnegative in the real world, for example, biological systems, chemical process, economic systems, and so on
Switched positive linear systems (SPLSs) with respect to the Schrödinger operator which consist of subsolutions of the stationary Schrödinger equation are found in many practical systems
The current results mainly concern the uniqueness of the common Schrödinger linear copositive Lyapunov function for switched positive linear systems (SPLSs) and stabilization design of SPLSs based on multiple Schrödinger Lyapunov functions

Summary

Introduction

It is well known that there exists a large class of systems whose states are always nonnegative in the real world, for example, biological systems, chemical process, economic systems, and so on. Switched positive linear systems (SPLSs) with respect to the Schrödinger operator which consist of subsolutions of the stationary Schrödinger equation are found in many practical systems. They have board applications in TCP congestion control, formation flying, and image processing [ ], to list a few. The switching law design of switched systems with respect to Schrödinger operator is always one of the topics of general interest [ , ]. Based on the above discussions, this paper addresses the state-feedback switching design of SPLSs, which contain unstable subsystems. In Section , we shall consider the stability of continuous-time systems and design the state-feedback switching law.

Ce vt x

Then we have

The above inequality verifies