Natural observers for second order lumped and distributed parameter systems using parameter-dependent Lyapunov functions

The aim of the paper is to present an alternative method for designing natural observers for linear second order systems (lumped and distributed parameter) without resorting to a first order formulation. This has the advantage of utilizing the algebraic structure that second order systems enjoy. The proposed scheme ensures that the derivative of the estimated "position" is indeed the estimate of the "velocity" component. A parameter-dependent Lyapunov function is utilized that ensures exponential convergence of the state estimation errors.

[1]  R. Skelton.  Dynamic Systems Control: Linear Systems Analysis and Synthesis , 1988 .

[2]  Hans Zwart,et al.  An Introduction to Infinite-Dimensional Linear Systems Theory , 1995, Texts in Applied Mathematics.

[3]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[4]  Frank L. Lewis,et al.  Optimal Control , 1986 .

[5]  Mark J. Balas,et al.  Do all linear flexible structures have convergent second-order observers? , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[6]  B.N. Datta,et al.  Multi-input partial eigenvalue assignment for the symmetric quadratic pencil , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[7]  S. Elhay,et al.  An algorithm for the partial multi-input pole assignment problem of a second-order control system , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[8]  W. Gawronski.  Dynamics and control of structures : a modal approach , 1998 .

[9]  B. Datta,et al.  Single-Input Partial Pole-Assignment in Gyroscopic Quadratic Matrix and Operator Pencils , 2000 .

[10]  B. Anderson,et al.  Optimal control: linear quadratic methods , 1990 .

[11]  Wodek Gawronski,et al.  Dynamics and Control of Structures , 1998 .

[12]  J. L. Lions,et al.  Control of Systems Governed by Parabolic Partial Differential Equations , 1971 .

[13]  J. Wloka,et al.  Partial differential equations: Strongly elliptic differential operators and the method of variations , 1987 .