H∞ Filter Design for State Estimation and Unknown Inputs Reconstruction of a Class of Nonlinear systems

We consider a novel method to design a H∞ filter for a class of nonlinear systems subject to unknown inputs. First, we rewrite the system dynamics as a descriptor system. Then, we design a robust H∞ reduced-order filter to estimate both state variables and unknown inputs at the same time. Based on a Lyapunov functional, we derive a sufficient condition for existence of the designed filter which requires solving a nonlinear matrix inequality. The achieved condition is further formulated in terms of a linear matrix inequality (LMI) that is straightforward to solve by popular methods. Finally, the proposed filter is illustrated with an example.

[1]  Fanglai Zhu,et al.  State estimation and unknown input reconstruction via both reduced-order and high-order sliding mode observers☆ , 2012 .

[2]  Thomas Gustafsson,et al.  Nonlinear observer design for a class of Lipschitz time-delay systems with unknown inputs: LMI approach , 2011, 2011 XXIII International Symposium on Information, Communication and Automation Technologies.

[3]  Mohamed Darouach,et al.  H∞ observers design for a class of nonlinear singular systems , 2011, Autom..

[4]  J. Lam,et al.  H/sub /spl infin// filtering for singular systems , 2003 .

[5]  Lei Zhou,et al.  Robust Stability of Singularly Perturbed Descriptor Systems With Nonlinear Perturbation , 2011, IEEE Transactions on Automatic Control.

[6]  Mohamed Darouach,et al.  Kalman filtering with unknown inputs via optimal state estimation of singular systems , 1995 .

[7]  W. Marsden.  I and J , 2012 .

[8]  Damien Koenig,et al.  Observer design for unknown input nonlinear descriptor systems via convex optimization , 2006, IEEE Transactions on Automatic Control.

[9]  Hieu Minh Trinh,et al.  State and input simultaneous estimation for a class of nonlinear systems , 2004, Autom..

[10]  Shengyuan Xu,et al.  Reduced-order H∞ filtering for singular systems , 2007, Syst. Control. Lett..

[11]  Shengyuan Xu,et al.  H∞ filtering for singular systems , 2003, IEEE Trans. Autom. Control..

[12]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.

[13]  M. Saif,et al.  Unknown input observer design for a class of nonlinear systems: an LMI approach , 2006, American Control Conference.

[14]  Mohamed Darouach,et al.  H∞ Unbiased Filtering for Linear Descriptor Systems via LMI , 2009, IEEE Trans. Autom. Control..

[15]  João Yoshiyuki Ishihara,et al.  Robust state prediction for descriptor systems , 2008, Autom..

[16]  Lei Zhou,et al.  A note on the existence of a solution and stability for Lipschitz discrete-time descriptor systems , 2011, Autom..

[17]  Mohamed Darouach,et al.  A controller design based on a functional H∞ filter for descriptor systems: The time and frequency domain cases , 2012, Autom..