Robust filtering for systems with state-dependent uncertainties and application to a class of tunnel diode circuits

The paper is concerned with the problem of robust filtering for a class of systems with state-dependent uncertainties and energy-bounded disturbance. The state-dependent uncertainties can more precisely describe many practical dynamic systems with parameters varying with system states, such as spring stiffness, nonlinear resistor and friction coefficient. A non-quadratic Lyapunov function is adopted, upon which the sufficient condition for the filtering performance analysis is first derived. Then, the parameter-dependent full-order filter is designed such that the corresponding filtering error system is globally asymptotically stable and guarantees a noise attenuation performance index. A numerical example of a class of tunnel diode circuit systems is provided to show the effectiveness of the derived theoretical results.

[1]  Graziano Chesi,et al.  Robust stability of time-varying polytopic systems via parameter-dependent homogeneous Lyapunov functions , 2007, Autom..

[2]  Huijun Gao,et al.  A delay-dependent approach to robust H∞ filtering for uncertain discrete-time state-delayed systems , 2004, IEEE Trans. Signal Process..

[3]  Manfred Morari,et al.  Robust constrained model predictive control using linear matrix inequalities , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[4]  Huijun Gao,et al.  New results on H∞ filtering for fuzzy systems with interval time-varying delays , 2011, Inf. Sci..

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

[6]  D. Bernstein,et al.  Steady-state kalman filtering with an H∞ error bound , 1989, 1989 American Control Conference.

[7]  Lihua Xie,et al.  Robust Kalman filtering for uncertain systems , 1994 .

[8]  P. Peres,et al.  Robust ℋ∞-Filtering Design with Pole Placement Constraint via Linear Matrix Inequalities , 1999 .

[9]  Huijun Gao,et al.  H ∞ filter design for discrete delay systems: a new parameter-dependent approach , 2009, Int. J. Control.

[10]  P. Peres,et al.  LMI approach to the mixed H/sub 2//H/sub /spl infin// filtering design for discrete-time uncertain systems , 2001 .

[11]  Fuwen Yang,et al.  Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noises , 2002, IEEE Trans. Autom. Control..

[12]  Petros G. Voulgaris,et al.  On optimal ℓ∞ to ℓ∞ filtering , 1995, Autom..

[13]  Hamid Reza Karimi,et al.  Local capacity H∞ control for production networks of autonomous work systems with time-varying delays , 2009, 2009 European Control Conference (ECC).

[14]  Hamid Reza Karimi,et al.  Local Capacity $H_{\infty}$ Control for Production Networks of Autonomous Work Systems With Time-Varying Delays , 2010, IEEE Transactions on Automation Science and Engineering.

[15]  Jingxin Zhang,et al.  All H∞ singular and normal filter design for uncertain singular systems , 2009, 2009 Chinese Control and Decision Conference.

[16]  Emilia Fridman,et al.  Robust H∞ filtering of linear systems with time-varying delay , 2003, IEEE Trans. Autom. Control..

[17]  Lihua Xie,et al.  H∞ filtering of 2-D discrete systems , 2000, IEEE Trans. Signal Process..

[18]  Fuwen Yang,et al.  Robust H/sub /spl infin// filtering for stochastic time-delay systems with missing measurements , 2006, IEEE Transactions on Signal Processing.

[19]  I. E. Zuber,et al.  Vector control design for robust stabilization of a class of uncertain systems , 2009 .

[20]  Peng Shi,et al.  Hinfinity output feedback control design for uncertain fuzzy singularly perturbed systems: an LMI approach , 2004, Autom..

[21]  D. Bernstein,et al.  Steady-state Kalman filtering with an H ∞ error bound , 1989 .

[22]  E. Boukas,et al.  Exponential H∞ filtering for uncertain discrete‐time switched linear systems with average dwell time: A µ‐dependent approach , 2008 .

[23]  Solomon Lefschetz,et al.  Stability by Liapunov's Direct Method With Applications , 1962 .

[24]  Peng Shi,et al.  Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters , 1999, IEEE Trans. Autom. Control..

[25]  Fuwen Yang,et al.  Robust H-infinity filtering for stochastic time-delay systems with missing measurements , 2006 .