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This paper investigates the minimum dwell time for switched linear systems. It is shown that a sequence of upper bounds of the minimum dwell time can be computed by exploiting homogeneous polynomial Lyapunov functions and convex optimization problems based on linear matrix inequalities (LMIs). This sequence is obtained by adopting two possible representations of homogeneous polynomials, one based...
A polynomial approach to deal with stability analysis of polynomial switched systems, i.e., polynomial continuous systems with switching signals, using dissipation inequalities under arbitrary switching is presented. It is shown that the representation of the original switched problem into a continuous polynomial systems allows us to use the dissipation inequality for polynomial systems. With this...
This paper investigates the stability of (switched) polynomial systems. Using semi-tensor product of matrices, the paper developed two tools for testing the stability of a (switched) polynomial system. First, a way to convert a product of multivariable polynomials into a canonical form. Second, an easily verifiable sufficient condition to justify whether a multi-variable polynomial is positive definite...
The problem of feedback stabilization for a class of switched nonlinear systems is considered using polynomial Lyapunov function, and two methods are presented based on sum of square decomposition. The first is direct method and feedback controllers can be obtained by solving feasibility problem of sum of square program. The second method is iterative method and feedback controllers can be obtained...
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