A Matrix Pencil Formulation for Nonconservative Realization of Scaling-Based Controllers for Feedforward-Like Systems

• Published in: IEEE transactions on automatic control Vol. 69; no. 1; pp. 261 - 274
• Main Authors: Krishnamurthy, Prashanth, Khorrami, Farshad
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Control design; Eigenvalues; Eigenvalues and eigenfunctions; Feedforward control; High gain; Linear matrix inequalities; Matrix methods; Nonlinear dynamical systems; Nonlinear systems; Observers; Output feedback; output feedback and observer; robust control; Scaling
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2023.3274915

We develop a general matrix pencil-based approach for efficient nonconservative realization of dual dynamic high-gain scaling-based control designs for a class of uncertain feedforward-like nonlinear systems. It is shown that the control design can be cast into a set of matrix pencil-based subproblems capturing the detailed system structure, state dependence structure of uncertain terms, and precise roles of design freedoms in the context of detailed structures of Lyapunov inequalities. The design freedoms in the dynamic high-gain scaling-based design are extracted in terms of eigenvalues of the formulated matrix pencil structures. It is seen that the proposed matrix pencil-based approach greatly reduces design conservatism and algebraic complexity compared with prior results on dynamic high-gain scaling-based control designs.