On the Numerical Solution of Differential Linear Matrix Inequalities

This paper presents a novel approach for the numerical solution of differential linear matrix inequalities. The solutions are searched in the class of piecewise-quadratic functions with symmetric matrix coefficients to be determined. To limit the numbers of unknowns, congruence constraints are considered to guarantee continuity of the solution and of its derivative. In Example section, some control problems involving differential linear matrix inequalities are considered and solved in order to compare the proposed approach with alternative approximation methods adopted in the literature.

[1]  Corentin Briat,et al.  Stability analysis and stabilization of stochastic linear impulsive, switched and sampled-data systems under dwell-time constraints , 2016, Autom..

[2]  Patrizio Colaneri,et al.  Differential linear matrix inequality in optimal sampled-data control , 2019, Autom..

[3]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[4]  Dimitri Peaucelle,et al.  SEDUMI INTERFACE 1.02: a tool for solving LMI problems with SEDUMI , 2002, Proceedings. IEEE International Symposium on Computer Aided Control System Design.

[5]  Francesco Amato,et al.  An Observer-Based Output Feedback Controller for the Finite-Time Stabilization of Markov Jump Linear Systems , 2019, IEEE Control Systems Letters.

[6]  Francesco Amato,et al.  Hybrid architecture for vehicle lateral collision avoidance , 2018, IET Control Theory & Applications.

[7]  Kim-Chuan Toh,et al.  SDPT3 -- A Matlab Software Package for Semidefinite Programming , 1996 .

[8]  Uri Shaked,et al.  A new bounded real lemma representation for the continuous-time case , 2001, IEEE Trans. Autom. Control..

[9]  F. Amato,et al.  Finite-Time Stability , 2018 .

[10]  Knud D. Andersen,et al.  The Mosek Interior Point Optimizer for Linear Programming: An Implementation of the Homogeneous Algorithm , 2000 .

[11]  Gabriela W. Gabriel,et al.  Optimal and Robust Sampled-Data Control of Markov Jump Linear Systems: A Differential LMI Approach , 2018, IEEE Transactions on Automatic Control.

[12]  Francesco Amato,et al.  Finite-Time Stability and Control , 2013 .

[13]  Gabriela W. Gabriel,et al.  Differential Linear Matrix Inequalities Optimization , 2019, IEEE Control Systems Letters.

[14]  Francesco Amato,et al.  Input-output finite-time stability of linear systems , 2009, 2009 17th Mediterranean Conference on Control and Automation.

[15]  Corentin Briat.  Convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampled-data systems under dwell-time constraints , 2013, Autom..

[16]  Francesco Amato,et al.  Annular Finite-Time Stabilization of Stochastic Linear Time-Varying Systems , 2018, 2018 IEEE Conference on Decision and Control (CDC).