A New Robust Nonfragile Controller Design Scheme for a Class of Hybrid Systems through Piecewise Affine Models

This paper investigates the robust nonfragile control problem for a class of discrete-time hybrid systems based on piecewise affine models. The objective is to develop an admissible piecewise affine nonfragile controller such that the resulting closed-loop system is asymptotically stable with robust performance . By employing a state-control augmentation methodology, some new sufficient conditions for the controller synthesis are formulated based on piecewise Lyapunov functions (PLFs). The controller gains can be obtained via solving a set of linear matrix inequalities. Simulation examples are finally presented to demonstrate the feasibility and effectiveness of the proposed approaches.

[1]  Jorge M. Gonçalves,et al.  Reachability analysis of continuous-time piecewise affine systems , 2008, Autom..

[2]  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.

[3]  Ju H. Park,et al.  Non-fragile synchronization control for complex networks with additive time-varying delays , 2015, Complex..

[4]  L. Rodrigues,et al.  Non-fragile state-feedback control of uncertain piecewise-affine slab systems with input constraints: a convex optimisation approach , 2014 .

[5]  Ju H. Park.  Robust non-fragile control for uncertain discrete-delay large-scale systems with a class of controller gain variations , 2004, Appl. Math. Comput..

[6]  Alberto Bemporad,et al.  Observability and controllability of piecewise affine and hybrid systems , 2000, IEEE Trans. Autom. Control..

[7]  Alessandro N. Vargas,et al.  Optimal Control of DC-DC Buck Converter via Linear Systems With Inaccessible Markovian Jumping Modes , 2016, IEEE Transactions on Control Systems Technology.

[8]  Jianbin Qiu,et al.  New approach to delay-dependent H ∞ filtering for discrete-time Markovian jump systems with time-varying delay and incomplete transition descriptions , 2013 .

[9]  Hairong Dong,et al.  Robust Adaptive Nonsingular Terminal Sliding Mode Control for Automatic Train Operation , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[10]  Nathan van de Wouw,et al.  Reconfigurable control of piecewise affine systems with actuator and sensor faults: Stability and tracking , 2011, Autom..

[11]  Jianbin Qiu,et al.  A Novel Approach to Reliable Control of Piecewise Affine Systems With Actuator Faults , 2017, IEEE Transactions on Circuits and Systems II: Express Briefs.

[12]  Fuad E. Alsaadi,et al.  Design of non-fragile state estimators for discrete time-delayed neural networks with parameter uncertainties , 2016, Neurocomputing.

[13]  M. Morari,et al.  Stability and stabilization of piecewise affine and hybrid systems: an LMI approach , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[14]  Y. Jia,et al.  Non-fragile dynamic output feedback control for linear systems with time-varying delay , 2009 .

[15]  Yolanda Vidal,et al.  Passive fault tolerant control strategy in controlled wind turbines , 2016, 2016 3rd Conference on Control and Fault-Tolerant Systems (SysTol).

[16]  Jianbin Qiu,et al.  Fixed-Order Piecewise-Affine Output Feedback Controller for Fuzzy-Affine-Model-Based Nonlinear Systems With Time-Varying Delay , 2017, IEEE Transactions on Circuits and Systems I: Regular Papers.

[17]  Victor Sreeram,et al.  Fuzzy-Model-Based Nonfragile Control for Nonlinear Singularly Perturbed Systems With Semi-Markov Jump Parameters , 2018, IEEE Transactions on Fuzzy Systems.

[18]  Jianbin Qiu,et al.  A Novel Approach to Reliable Output Feedback Control of Fuzzy-Affine Systems With Time Delays and Sensor Faults , 2017, IEEE Transactions on Fuzzy Systems.

[19]  Shankar P. Bhattacharyya,et al.  Robust, fragile or optimal? , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[20]  Xingang Zhao.  Piecewise H ∞ Static Output Feedback Controller Design for Nonlinear Systems Based on TS Affine Fuzzy Models , 2015 .

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

[22]  Xingang Zhao.  Piecewise H-infinity Static Output Feedback Controller Design for Nonlinear Systems Based on T-S Affine Fuzzy Models , 2015 .

[23]  Shuping He,et al.  Non-fragile passive controller design for nonlinear Markovian jumping systems via observer-based controls , 2015, Neurocomputing.

[24]  Alberto Bemporad,et al.  Control of systems integrating logic, dynamics, and constraints , 1999, Autom..

[25]  Sheng Liu,et al.  Robust Course Keeping Control of a Fully Submerged Hydrofoil Vessel without Velocity Measurement: An Iterative Learning Approach , 2017 .

[26]  M. Kchaou,et al.  Non-fragile H∞ output feedback control design for continuous-time fuzzy systems. , 2015, ISA transactions.

[27]  Jianliang Wang,et al.  Non-fragile Hinfinity control for linear systems with multiplicative controller gain variations , 2001, Autom..

[28]  Jun-ichi Imura.  Classification and stabilizability analysis of bimodal piecewise affine systems , 2002 .

[29]  Shouming Zhong,et al.  A descriptor system approach to non-fragile H∞ control for uncertain fuzzy neutral systems , 2009, Fuzzy Sets Syst..

[30]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[31]  Manfred Morari,et al.  Analysis of discrete-time piecewise affine and hybrid systems , 2002, Autom..

[32]  Jianbin Qiu,et al.  A New Design of $H$ -Infinity Piecewise Filtering for Discrete-Time Nonlinear Time-Varying Delay Systems via T–S Fuzzy Affine Models , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[33]  Mao Wang,et al.  Robust H-Infinity Stabilization and Resilient Filtering for Discrete-Time Constrained Singular Piecewise-Affine Systems , 2015 .

[34]  Xue-Jun Xie,et al.  Global Adaptive Stabilization and Tracking Control for High-Order Stochastic Nonlinear Systems With Time-Varying Delays , 2018, IEEE Transactions on Automatic Control.

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

[36]  Chee Peng Lim,et al.  Synchronization of discrete-time Markovian jump complex dynamical networks with random delays via non-fragile control , 2016, J. Frankl. Inst..

[37]  Renquan Lu,et al.  Passivity-based non-fragile control for Markovian jump systems with aperiodic sampling , 2015, Syst. Control. Lett..

[38]  Tao Li,et al.  A new approach to robust and non-fragile Hinfinity control for uncertain fuzzy systems , 2007, Inf. Sci..

[39]  Ju H. Park,et al.  Distributed Impulsive Quasi-Synchronization of Lur’e Networks With Proportional Delay , 2019, IEEE Transactions on Cybernetics.

[40]  S. Pettersson,et al.  Exponential Stability of Hybrid Systems Using Piecewise Quadratic Lyapunov Functions Resulting in LMIs , 1999 .

[41]  Cong-Ran Zhao,et al.  A Combined Homogeneous Domination and Sign Function Approach to Output-Feedback Stabilization of Stochastic High-Order Nonlinear Systems , 2014, IEEE Transactions on Automatic Control.

[42]  Hamid Reza Karimi,et al.  Improved Stability and Stabilization Results for Stochastic Synchronization of Continuous-Time Semi-Markovian Jump Neural Networks With Time-Varying Delay , 2017, IEEE Transactions on Neural Networks and Learning Systems.