Reference tracking and transient response shaping of uncertain quasi one-sided Lipschitz nonlinear systems

Abstract

This work addresses the reference tracking problem for uncertain systems with quasi one-sided Lipschitz nonlinearity. The uncertainty is assumed to be of a norm bound parametric type. Moreover, transient response shaping using the concept of ‘return time’ is also proposed. The controller design relies on the solution of Linear Matrix Inequalities (LMIs) and hence is computationally efficient. The proposed control law is linear in states, and thus the implementation is often straightforward. To illustrate the capability and simplicity of the proposed theory, three design examples are included.

Keywords:

• Reference tracking
• norm bound parametric uncertainty
• return time
• linear matrix inequalities
• quasi one-sided Lipschitz nonlinearity

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. An algorithm is said to have polynomial time complexity if its running time is upper bounded by a polynomial expression in the size of the input for the algorithm. Cobham's thesis (Cobham, 1965) states that polynomial time (Goldreich, 2006) is a synonym for ‘tractable’, ‘feasible’, ‘efficient’, or ‘fast’.

Additional information

Notes on contributors

Arunima Mukherjee

Arunima Mukherjee received her Bachelor's degree (Electrical & Electronics) in 2010 from U.P Technical University, Lucknow, India. She received her Master's degree from Indian Institute of Engineering Science Technology, Shibpur, India in 2013. She begun her PhD at the same institute in 2015 and currently working towards completing it. Her research interests are in nonlinear system, systems with time delays, switched systems and data-driven system modelling.

Aparajita Sengupta

Aparajita Sengupta is a Professor in the department of Electrical Engg at Indian Institute of Engineering Science Technology, Shibpur, India. She received her Bachelor's degree from Jadavpur University, Calcutta, W.B, India in 1992. She received her Master's and PhD degree from Indian Institute of Technology, Kharagpur, W.B, India in 1994 and 1997, respectively. Her research interests include nonlinear control, nonlinear estimation, application of artificial intelligence, Linear Matrix Inequalities in control, robust control and time delays systems.