Sensor blending and control allocation for non-square linear systems to achieve negative imaginary dynamics

Parijat Bhowmick, Alexander Lanzon

Research output: Contribution to journalConference articlepeer-review


This paper deals with the design of static pre- and post- compensators to transform stable, non-square LTI systems into the class of strongly strict negative imaginary systems. The pre-compensator plays the role of a control allocator while the post-compensator does sensor blending in order to make a non-square system square along with satisfying the strongly strict negative imaginary property. A specific structure of the post-compensator is also given that guarantees a feasible solution of the LMI conditions when applied to systems with number of outputs greater than or equal to number of inputs. The proposed pre- and post- compensators can also stabilize a non-square plant in closed-loop upon satisfying a particular DC-gain condition and furthermore, they can be utilized to develop a simple constant input tracking framework for non-square systems. The LMI-based design methodology offers a numerically tractable solution framework and hence the easy implementation of the proposed scheme in practical applications. Illustrative examples are provided throughout the paper to demonstrate the usefulness of the proposed results in widening the scope of the negative imaginary theory to non-square LTI systems (e.g. safety-critical systems having redundant sensors and actuators).

Original languageEnglish
Pages (from-to)4629-4634
Number of pages6
Issue number2
Publication statusPublished - 14 Apr 2021
Event21st IFAC World Congress 2020 - Berlin, Germany
Duration: 12 Jul 202017 Jul 2020


  • DC-gain
  • LMIs
  • Non-square plants
  • Positive feedback
  • Reference tracking
  • Strongly strict negative imaginary systems


Dive into the research topics of 'Sensor blending and control allocation for non-square linear systems to achieve negative imaginary dynamics'. Together they form a unique fingerprint.

Cite this