Reachability analysis is a powerful formal method for analysis of concurrent and distributed nite state systems. It suuers from the state space explosion problem, however: the state space of a system can be far too large to be completely generated. This report considers two promising methods, Valmari's stubborn set method and Godefroid's sleep set method, to avoid generating all of the state sp...

The paper studies controllability problems for the reachable set of a differential inclusion. These were originally motivated by models of control of a flock of animals. Conditions are derived for the existence or nonexistence of a strategy which confines the reachable set within a given bounded region, at all sufficiently large times. Steering problems and the asymptotic shape of the reachable...

In this paper we study the geometrical properties of the set of reachable states of a single input discrete– time LTI system with positive controls. This set is a cone and it can be expressed as the direct sum of a linear subspace and a proper cone. In order to give a complete geometrical characterization of the reachable set, we provide a formula to evaluate the dimension of the largest reacha...

Abstract. One of the most interesting dynamical systems used in numerical analysis is the QR algorithm. An added maneuver to improve the convergence behavior is the QR iteration with shift which is of fundamental importance in eigenvalue computation. This paper is a theoretical study of the set of all isospectral matrices “reachable” by the dynamics of QR algorithm with shift. A matrix B is sai...

In this paper, Cloud classification has been demonstrated using accessibility factor of distinct Cloud clusters. Group and non-group Cloud structures have been classified using its direction of scope of activities. Each type of Cloud is further divided into different clusters based on its unique status, such as reachable cluster, non-reachable cluster, basin cluster, momentary cluster, and init...

Among the various critical systems that are worth to be formally analyzed, a wide set consists of controllers for dynamical systems. Those programs typically execute an infinite loop in which simple computations update internal states and produce commands to update the system state. Those systems are yet hardly analyzable by available static analysis method, since, even if performing mainly lin...

In this paper, we address regional stability and performance analysis on linear control systems with linear anti-windup augmentation. We use LMIs to compute 1) an upper bound for the nonlinear L2 gain, 2) an estimate of the reachable set under norm bounded exogenous input and 3) an estimate of the domain of attraction with zero input. The problems are studied in a general setting where the only...