Abstract
The objective of this paper is to introduce the notion of parametric quadratic stabilizability (PQ-stabilizability) of nonlinear control systems x ̇ = [A + ΔA(p)]x +[B + Δ(p)]φ(u) . When we consider nonlinear systems, reference inputs and disturbances may alter dynamics in an essential way by moving the equilibrium to a new location, or destroying it altogether. For this reason, when we consider quadratic stabilizability (Q-stabilizability) of nonlinear systems, we need to combine the two concepts of parametric stability and Q-stabilizability, and consider PQ-stabilizability. When nonlinear function φ belongs to a subclass of passive functions, it is shown that the necessary and sufficient condition for quadratic stabilizability (Q-stabilizability) of linear systems via dynamic state feedback, which was derived by Zhou and Khargonekar, is also a necessary and sufficient condition for that of nonlinear systems considered in this paper. Moreover, when nonlinear function φ belongs to a subclass of incresing functions and when ΔB = 0, it shown that the necessary and sufficient condition for Q-stabilizability of linear systems via static state feedback, which was derrived by Petersen, is also a necessary and sufficient condition for that of nonlinear systems considered in this paper.
Published Version
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