On Stability Cones for Quadratic Systems of Differential Equations
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New sufficient conditions of conditional stability of the trivial solution of a system of quadratic ordinary differential equations are obtained. For the homogeneous system the domain of unlocal stability is also found (it is a cone). This domain is then used for design of piecewise linear (discontinuous) control laws on output for a bilinear control system of any order. Thus, a system closed by such discontinuous feedback becomes globally stable in the Lyapunov sense on the whole state space. Examples are given.
Key words and phrases.System of quadratic ordinary differential equations bilinear control system linear control law stability cone feedback
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