| Control and Dynamical Systems (2008) | |||||||||||||||
Abstract | |||||||||||||||
| Consider the system with two output maps ˙x(t) = f(x(t), u(t)) (1) y(t) = h(x(t)), w(t) = g(x(t)), with state x ∈ R and controls u measurable essentially bounded functions into R m. Assume that the function f: R n × R m → R n is locally Lipschitz, and that the system is forward complete. Assume that the output maps h: R n → R py and g: R n → R pw are locally Lipschitz. The Euclidean norm in a space R k is denoted simply by |·|. If z is a function defined on a real interval containing [0, t], �z � [0,t] is the sup norm of the restriction of z to [0, t], that is �z � [0,t] = ess sup {|z(t) | : t ∈ [0, t]}. A function γ: R≥0 → R≥0 is of class K (denoted γ ∈ K) if it is continuous, positive definite, and strictly increasing; and is of class K ∞ if in addition it is unbounded. A function β: R≥0 × R≥0 → R≥0 is of class KL if for each fixed t ≥ 0, β(·, t) is of class K and for each fixed s ≥ 0, β(s, t) decreases to zero as | |||||||||||||||
Publication details | |||||||||||||||
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