Non-fragile reliable D-stabilization for delta operator switched linear systems

Abstract This paper is concerned with the non-fragile reliable D - stabilization problem of a class of delta operator switched linear systems with actuator faults, in terms of linear matrix inequalities (LMIs). Firstly, to handle the determination problem of the decay rate of a delta operator system in the process of D - stabilizing , the theory of first-order LMI regions is proposed. Secondly, to deal with the uncertain matrices multiplication phenomenon appearing in non-fragile reliable control, a new approach is proposed. Based on the average dwell time technique and the two new methods mentioned above, the state feedback controller and the switching law are designed to guarantee that all the closed-loop poles of each mode lie in a specified disk and the closed-loop switched system is exponentially stable. Finally, the validity and feasibility of the proposed approach are illustrated by a flight control system example.

[1]  Alessandro Astolfi,et al.  Stabilization of continuous-time switched nonlinear systems , 2008, Syst. Control. Lett..

[2]  Sang Bong Kim,et al.  Pole assignment in a specified disk , 1987 .

[3]  Pierre Apkarian,et al.  Robust pole placement in LMI regions , 1999, IEEE Trans. Autom. Control..

[4]  J. Bernussou,et al.  A new robust D-stability condition for real convex polytopic uncertainty , 2000 .

[5]  Zhendong Sun.  A Note on Marginal Stability of Switched Systems , 2008, IEEE Trans. Autom. Control..

[6]  Zhendong Sun.  Stabilizability and insensitivity of switched linear systems , 2004, IEEE Trans. Autom. Control..

[7]  Paul C. Peterson.  Dalton Trumbo: Blacklisted Hollywood Radical Larry Ceplair and Christopher Trumbo. University Press of Kentucky, 2015. , 2017 .

[8]  Pascal Gahinet,et al.  H/sub /spl infin// design with pole placement constraints: an LMI approach , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[9]  S. Gutman,et al.  A general theory for matrix root-clustering in subregions of the complex plane , 1981 .

[10]  Bin Jiang,et al.  Fault Tolerance Analysis for Switched Systems Via Global Passivity , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[11]  Chien-Hua Lee.  D-stability of continuous time-delay systems subjected to a class of highly structured perturbations , 1995, IEEE Trans. Autom. Control..

[12]  G. Goodwin,et al.  Improved finite word length characteristics in digital control using delta operators , 1986 .

[13]  Graham C. Goodwin,et al.  Digital control and estimation : a unified approach , 1990 .

[14]  Marion Hersh,et al.  The zeros and poles of delta operator systems , 1993 .

[15]  Shankar P. Bhattacharyya,et al.  Robust, fragile, or optimal? , 1997, IEEE Trans. Autom. Control..

[16]  Yongduan Song,et al.  Fault Detection Filtering for Nonlinear Switched Stochastic Systems , 2016, IEEE Transactions on Automatic Control.

[17]  Yuanqing Xia,et al.  Low frequency positive real control for delta operator systems , 2012, Autom..

[18]  Xiaojie Su,et al.  Dissipativity-Based Filtering for Fuzzy Switched Systems With Stochastic Perturbation , 2016, IEEE Transactions on Automatic Control.

[19]  Wei Xing Zheng,et al.  Dissipativity-Based Sliding Mode Control of Switched Stochastic Systems , 2013, IEEE Transactions on Automatic Control.

[20]  Jun Zhao,et al.  On stability, L2-gain and Hinfinity control for switched systems , 2008, Autom..

[21]  Bengt Lennartson,et al.  Numerical Sensitivity of Linear Matrix Inequalities Using Shift and Delta Operators , 2012, IEEE Transactions on Automatic Control.

[22]  Kevin Guelton,et al.  Robust pole placement controller design in LMI region for uncertain and disturbed switched systems , 2008 .

[23]  Jun Zhao,et al.  Passivity and stability of switched systems: A multiple storage function method , 2008, Syst. Control. Lett..

[24]  Tsu-Tian Lee,et al.  Optimal static output feedback simultaneous regional pole placement , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[25]  Pedro Luis Dias Peres,et al.  An improved LMI condition for robust D-stability of uncertain polytopic systems , 2003, IEEE Trans. Autom. Control..

[26]  Ülo Nurges.  Robust pole assignment via reflection coefficients of polynomials , 2006, Autom..

[27]  Young Hoon Joo,et al.  Lifted versions of robust D-stability and D-stabilisation conditions for uncertain polytopic linear systems , 2012 .

[28]  Magdi S. Mahmoud,et al.  Guaranteed-cost reliable control with regional pole placement of a power system , 2011, J. Frankl. Inst..

[29]  J. Geromel,et al.  Stability and stabilization of discrete time switched systems , 2006 .

[30]  G. Goodwin,et al.  High-speed digital signal processing and control , 1992, Proc. IEEE.

[31]  Germain Garcia,et al.  Pole assignment for uncertain systems in a specified disk by output feedback , 1996, Math. Control. Signals Syst..

[32]  Wook Hyun Kwon,et al.  Delay-dependent robust Hinfinity control for uncertain systems with a state-delay , 2004, Autom..

[33]  Jian Chu,et al.  D-stability and D-stabilization of linear discrete time-delay systems with polytopic uncertainties , 2009, Autom..

[34]  A. Morse,et al.  Stability of switched systems with average dwell-time , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[35]  Huijun Gao,et al.  Robust H∞ filtering for switched linear discrete‐time systems with polytopic uncertainties , 2006 .

[36]  P. Gahinet,et al.  H∞ design with pole placement constraints: an LMI approach , 1996, IEEE Trans. Autom. Control..

[37]  William R. Perkins,et al.  Reliable control in the presence of sensor/actuator failures: a unified discrete/continuous approach , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[38]  Hongye Su,et al.  Generalized guaranteed cost control with D-stability and multiple output constraints , 2012, Appl. Math. Comput..

[39]  Peng Shi,et al.  $l_{2}-l_{\infty}$ Model Reduction for Switched LPV Systems With Average Dwell Time , 2008, IEEE Transactions on Automatic Control.

[40]  Yuanqing Xia,et al.  A Novel Delta Operator Kalman Filter Design and Convergence Analysis , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[41]  Piotr Suchomski.  Numerically robust delta-domain solutions to discrete-time Lyapunov equations , 2002, Syst. Control. Lett..

[42]  P. Dorato,et al.  Non-fragile controller design: an overview , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[43]  Tsu-Tian Lee,et al.  A New Approach to Optimal Regional Pole Placement , 1997, Autom..

[44]  Sophie Tarbouriech,et al.  Pole assignment in a disk for linear systems by static output feedback , 2003 .