Abstract:
For uniform absolute stability of nonlinear control systems in the class of nonstationary nonlinearities which satisfy sectorial constraints it is found that existence of a unique (for the class of systems) stringently convex Lyapunov function of quasiquadratic form is necessary and sufficient. A parametric class of simple piecewise quadratic Lyapunov functions and its kindred class of piecewise linear Lyapunov functions which also define the necessary and sufficient conditions for absolute stability of such systems are described. The level surfaces of these functions are centrally symmetrical convex polyhedrons.
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