Robust reference tracking and transient response shaping of a class of nonlinear systems

Abstract

This work examines stabilisation and reference tracking problems for uncertain deterministic as well as switched stochastic nonlinear systems. The concept of input state stability is employed here in the tracking problems. Additionally, an attempt is made to improve the transient performance of deterministic nonlinear systems by employing the notion of return time which is applicable to a broader class of nonlinearities. The transient performances are compared using the Integral Square Error (ISE). The control law is linear in states and thus is easy to implement. The optimisation problem is formulated in a framework of Linear Matrix Inequalities (LMIs). The proposed design is tested on simulation examples. The advantages are established on benchmark problems from the literature like Control of the Wing Rocket Aircraft and the Continuously Stirred Tank Chemical Reactor (CSTR). As per the author's knowledge, not much work is reported on these problems.

Keywords:

• Nonlinear systems
• linear matrix inequality
• reference tracking
• return time
• norm bounded parametric uncertainties
• switched stochastic nonlinear systems

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Arunima Mukherjee http://orcid.org/0000-0001-5205-4084

Additional information

Funding

This work was supported by IIEST, Shibpur.