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Reachability analysis of continuous-time piecewise affine systems ; Goncalves, Jorge in Automatica (2008), 44(12), 3189-3194 This paper proposes an algorithm for the characterization of reachable sets of states for continuous-time piecewise affine systems. Given a model of the system and a bounded set of possible initial states ... [more ▼] This paper proposes an algorithm for the characterization of reachable sets of states for continuous-time piecewise affine systems. Given a model of the system and a bounded set of possible initial states, the algorithm employs an LMI approach to compute both upper and lower bounds on reachable regions. Rather than performing computations in the state-space, this method uses impact maps to find the reachable sets on the switching surfaces of the system. This tool can then be used to deduce safety and performance results about the system. [less ▲] Detailed reference viewed: 133 (1 UL)Robust synchronization in networks of cyclic feedback systems ; Goncalves, Jorge ; in The proceedings of the 47th IEEE Conference on Decision and Control (2008) This paper presents a result on the robust synchronization of outputs of statically interconnected non-identical cyclic feedback systems that are used to model, among other processes, gene expression. The ... [more ▼] This paper presents a result on the robust synchronization of outputs of statically interconnected non-identical cyclic feedback systems that are used to model, among other processes, gene expression. The result uses incremental versions of the small gain theorem and dissipativity theory to arrive at an upper bound on the norm of the synchronization error between corresponding states, giving a measure of the degree of convergence of the solutions. This error bound is shown to be a function of the difference between the parameters of the interconnected systems, and disappears in the case where the systems are identical, thus retrieving an earlier synchronization result. [less ▲] Detailed reference viewed: 100 (2 UL)Reachability analysis of continuous time piecewise linear systems ; Goncalves, Jorge in Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference (2005) This paper presents a new approach to the reachability problem for a class of hybrid systems called Piecewise Linear Systems (PLS). The principal tool used is the impact map between switching surfaces ... [more ▼] This paper presents a new approach to the reachability problem for a class of hybrid systems called Piecewise Linear Systems (PLS). The principal tool used is the impact map between switching surfaces. The method consists of specifying a ellipsoidal set on the initial switching surface and finding upper- and lower-bound estimates of the possible reach sets using tools such as the S-procedure to set up linear matrix inequalities, of which numerical solutions are then computed. [less ▲] Detailed reference viewed: 99 (0 UL) |
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