New Approach to Fixed-Order Output-Feedback Control for Piecewise-Affine Systems

This paper studies the fixed-order piecewise-affine (PWA) output-feedback control of PWA systems in an $\mathscr {H}_{\infty }$ setup. In particular, the conventional output-feedback closed-loop system is first augmented with the introduction of the input vector, and a descriptor presentation of PWA system is acquired. Then, a bounded real lemma is derived for the resulting PWA system, which is realized by the construction of a smooth piecewise Lyapunov function and application of the S-procedure. Furthermore, by availing oneself of the descriptor formulation, the fixed-order PWA output-feedback controller synthesis is carried out in a unified framework. An illustrative example is provided to show the efficacy and impact of the proposed control design methodology in a Chua’s circuit.

[1]  I. Masubuchi,et al.  H∞ control for descriptor systems: A matrix inequalities approach , 1997, Autom..

[2]  Z. Luo,et al.  Computational complexity of a problem arising in fixed order output feedback design , 1997 .

[3]  Anders Rantzer,et al.  Computation of piecewise quadratic Lyapunov functions for hybrid systems , 1997, 1997 European Control Conference (ECC).

[4]  Jonathan P. How,et al.  Output feedback controller synthesis for piecewise-affine systems with multiple equilibria , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[5]  G. Feng.  Controller design and analysis of uncertain piecewise-linear systems , 2002 .

[6]  Chen Yu.  Reliable H~∞ Control for Affine Nonlinear Systems , 2003 .

[7]  Gang Feng.  Observer-based output feedback controller design of piecewise discrete-time linear systems , 2003 .

[8]  Marco Storace,et al.  Piecewise-linear approximation of nonlinear dynamical systems , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[9]  Stephen P. Boyd,et al.  Piecewise-affine state feedback for piecewise-affine slab systems using convex optimization , 2005, Syst. Control. Lett..

[10]  Gang Feng,et al.  Output Tracking of Piecewise-Linear Systems via Error Feedback Regulator With Application to Synchronization of Nonlinear Chua's Circuit , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[11]  Xiaofeng Liao,et al.  Stability of piecewise affine systems with application to chaos stabilization. , 2007, Chaos.

[12]  Gang Feng,et al.  Delay-Dependent ${H}_{\infty}$ Filtering of Piecewise-Linear Systems With Time-Varying Delays , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[13]  Luis Rodrigues,et al.  PWA H∞ controller synthesis for uncertain PWA slab systems , 2008, 2008 47th IEEE Conference on Decision and Control.

[14]  Xiaoyan Ma,et al.  A Basis-Function Canonical Piecewise-Linear Approximation , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[15]  Jianbin Qiu,et al.  Robust H∞ static output feedback control of discrete-time: Piecewise affine systems , 2009, 2009 IEEE International Conference on Control and Automation.

[16]  James Lam,et al.  Static output-feedback stabilization of discrete-time Markovian jump linear systems: A system augmentation approach , 2010, Autom..

[17]  Tingshu Hu,et al.  Estimation of Magnitude of Self-Induced Oscillations via Piecewise Quadratic Lyapunov Functions , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[18]  Hamid Reza Karimi,et al.  Robust Delay-Dependent $H_{\infty}$ Control of Uncertain Time-Delay Systems With Mixed Neutral, Discrete, and Distributed Time-Delays and Markovian Switching Parameters , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[19]  Omar D. Lifschitz,et al.  Application-Specific Processor for Piecewise Linear Functions Computation , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[20]  Jianbin Qiu,et al.  Approaches to robust ℋ︁∞ static output feedback control of discrete‐time piecewise‐affine systems with norm‐bounded uncertainties , 2011 .

[21]  Ali Karimpour,et al.  Hybrid Modeling of a DC-DC Series Resonant Converter: Direct Piecewise Affine Approach , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[22]  Mohamed Darouach,et al.  Novel bounded real lemma for discrete-time descriptor systems: Application to H∞ control design , 2012, Autom..

[23]  Mohammed Chadli,et al.  LMI Solution for Robust Static Output Feedback Control of Discrete Takagi–Sugeno Fuzzy Models , 2012, IEEE Transactions on Fuzzy Systems.

[24]  Ricardo C. L. F. Oliveira,et al.  Reduced-order dynamic output feedback control of continuous-time T-S fuzzy systems , 2012, Fuzzy Sets Syst..

[25]  Xiao‐Heng Chang.  A Descriptor Representation Approach , 2012 .

[26]  Jianbin Qiu,et al.  Static-Output-Feedback ${\mathscr H}_{\bm \infty }$ Control of Continuous-Time T - S Fuzzy Affine Systems Via Piecewise Lyapunov Functions , 2013, IEEE Transactions on Fuzzy Systems.

[27]  Yigang He,et al.  Finite-Time Synchronization of a Class of Second-Order Nonlinear Multi-Agent Systems Using Output Feedback Control , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[28]  Arash Nejadpak,et al.  Stabilizing Controller Design for Quasi-Resonant Converters Described by a Class of Piecewise Linear Models , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[29]  Young Hoon Joo,et al.  Periodically time-varying memory static output feedback control design for discrete-time LTI systems , 2014, Autom..

[30]  ByongChan Lim,et al.  Error Control and Limit Cycle Elimination in Event-Driven Piecewise Linear Analog Functional Models , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[31]  Patrizio Colaneri,et al.  Homogeneous Rational Lyapunov Functions for Performance Analysis of Switched Systems With Arbitrary Switching and Dwell Time Constraints , 2017, IEEE Transactions on Automatic Control.