Efficient computation of trajectories of switched affine systems becomes possible, if for any such hybrid system, we can manage to efficiently compute the sequence of switching times. Once the switching times have been computed, we can easily compute the trajectories between two successive switches as the solution of an affine ODE. Each switching time can be seen as a positive real root of an analytic function, thereby allowing for efficient computation by using root finding algorithms. These algorithms require a finite interval, within which to search for the switching time. In this paper, we study the problem of computing upper bounds on such switching times, and we restrict our attention to stable time-invariant affine systems. We provide semi-definite programming models to compute upper bounds on the time taken by the trajectories of an affine ODE to exit a set described as the intersection of a few generalized ellipsoids. Through numerical experiments, we show that the resulting bounds are tighter than bounds reported before, while requiring only a modest increase in computation time.
Decomposition Techniques for Bilinear Saddle Point Problems and Variational Inequalities with Affine Monotone Operators on Domains Given by Linear Minimization Oracles
Dimensionality Reduction of Affine Variational Inequalities Using Random Projections
Department of Electrical Engineering, Indian Institute of Technology Bombay（印度理工学院班加罗尔电子工程系）；Systems and Control Engineering, Indian Institute of Technology Bombay（印度理工学院班加罗尔系统与控制工程系）
A Douglas-Rachford Splitting Method for Solving Monotone Variational Inequalities in Linear-quadratic Dynamic Games
Rotterdam School of Management, Erasmus University（鹿特丹管理学院，伊拉斯姆斯大学）；Division of Decision and Control Systems, KTH Royal Institute of Technology（决策与控制系，皇家理工学院）；Delft Center for Systems and Control, Delft University of Technology（系统与控制中心，代尔夫特理工大学）
