Stability of Planar Switched Systems: The Linear Single Input Case

SIAM Journal on Control and Optimization (Impact Factor: 1.46). 06/2002; 41(1):89-112. DOI: 10.1137/S0363012900382837
Source: DBLP


We study the stability of the origin for the dynamical system ˙ x(t )= u(t)Ax(t )+( 1− u(t))Bx(t), where A and B are two 2 × 2 real matrices with eigenvalues having strictly negative real part, x ∈ R,. In the space of these parameters, the shape and the convexity of the region in which there is stability are studied. This bidimensional problem assumes particular interest since linear systems of higher dimensions can be reduced to our situation. Key words. stability, planar, random switching function, switched systems AMS subject classifications. 93D20, 37N35 PII. S0363012900382837

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    • "For n = 2 this approach led to a deep qualitative understanding of the problem in terms of the value function corresponding to the optimal control problem [21] (see also [22]). A dynamic programming approach [13] provided the first explicit expression for the value function for the case n = 2 [14] (see also [9] and the closely related work [5]). These issues are described in detail in the recent survey paper [12]. "
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