On the computation of the robust viability kernel for switched systems

Abstract

This paper presents an algorithm of computing the robust viability kernel for discrete‐time switched systems with arbitrary switching rule and bounded disturbance based on the robust one‐step set and Pontryagin difference. The algorithm can be implemented by performing the relevant set computations using polyhedral algebra and computational geometry software when switched systems are linear. In addition, we propose a method of computing inner approximation of the robust viability kernel for switched systems based on the set theory. The convergence of the iterative algorithm is proved using a null controllable set. Finally, two examples are provided to show the effectiveness of the proposed method.

Performance estimation of switched linear systems via n×(n+2) generalized coordinate transformations

“…For a given matrix A ∈ R n×n , let m = n + 2, P = (p i𝑗 ) m×m , and Y = (𝑦 i𝑗 ) n×m . According to Lemma 3, a family of mn equations can be obtained from matrix equation (5). For these equations, suppose 𝑦 i𝑗 are given constants to determine the values of p i𝑗 , i, 𝑗 = 1, • • • , m to satisfy each of the equations simultaneously.…”

“…Since switched systems provide a natural mathematic framework for modeling, control, and optimization of complex dynamical systems, switched systems theory has wide applications, such as switched electronic systems [2], cyberattacks [3], and robotic manipulators [4]. Switched systems have attracted considerable attention in the last decades [5][6][7][8][9][10][11][12][13].…”