Bumpless stabilisation of uncertain switched positive linear systems under synchronous and asynchronous switching

Abstract

This paper deals with stabilising uncertain Switched Positive Linear Systems (SPLSs) with a bumpless transfer controller. The contribution of this study is to improve switching controller robustness at the switching instances and also guarantee the $L_1$–gain performance of the positive systems. Positive systems are widespread; most of the biological, economic systems, disease, etc., have nonnegative variables belonging to this class of systems. Positive Systems modelling encounters different types of uncertainties; therefore, stability analysis and stabilisation of uncertain SPLSs are crucial in analysing positive systems. The stability of the SPLSs can be guarantee by using multiple copositive Lyapunov functions with the Dwell Time (DT) strategy. The stability of the SPLS has been investigated under synchronous and asynchronous switching modes. The so-called asynchronous switching means that the switches between the candidate controllers and system modes are asynchronous. Also, the $L_1$–gain performance of the system is derived. Finally, two illustrative examples are provided to demonstrate the proposed scheme’s effectiveness compared with the foremost existing solutions.

KEYWORDS:

• Switched positive linear systems (SPLSs)
• asynchronous switching
• bumpless transfer control
• dwell time
• interval uncertainty
• L1-gain

Disclosure statement

No potential conflict of interest was reported by the author(s).