Input–output finite-time stabilisation for periodic piecewise polynomial systems with nonlinear actuator faults: an observer-based approach

Abstract

This paper is concerned with the input–output finite-time (IO-FT) stabilisation problem for a class of continuous-time periodic piecewise polynomial systems (PPPSs) with immeasurable states and external disturbances via state estimation-based robust reliable controller. Firstly, to reflect the actuality, a parameter uncertainty that exhibits the random nature and the actuator faults with nonlinear character are considered in the addressed PPPSs and the control scheme, respectively. In detail, the randomness of uncertain parameters is portrayed by the stochastic variable and it is presumed to pursue the Bernoulli distributions. Secondly, to estimate the immeasurable states of PPPSs, a periodic piecewise polynomial observer is designed depending on the output of PPPSs. The main intent of this article is to devise a state estimation-based robust reliable controller to ascertain the IO-FT stabilisation of the PPPSs. Moreover, by bridging the Lyapunov stability theory, linear matrix inequality technique and IO-FT stability theory, the required IO-FT stabilisation conditions in the frame of linear matrix inequality are procured for the system under consideration. Eventually, simulation results of the addressed PPPSs are shown in line with the proposed analytical findings, revealing the competence, inherent capability and utility of the devised control protocol.

Keywords:

• Periodic piecewise polynomial systems
• randomly occurring uncertainties
• nonlinear actuator faults
• input–output finite-time stabilisation
• observer-based control

Disclosure statement

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

Data availability statement

Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.

Additional information

Funding

This work of R. Sakthivel and N. Aravinth were financially supported by Science and Engineering Research Board (SERB), Department of Science and Technology (DST), Government of India under Core Research Grant (CRG), Sanction No. CRG/2020/002844.