By Zhendong Sun
Switched linear platforms have loved a selected progress in curiosity because the Nineties. the massive quantity of knowledge and ideas hence generated have, previously, lacked a co-ordinating framework to concentration them successfully on a number of the primary concerns comparable to the issues of strong stabilizing switching layout, suggestions stabilization and optimum switching. This deficiency is resolved by way of this e-book which gains: nucleus of positive layout methods in line with canonical decomposition and forming a legitimate foundation for the systematic therapy of secondary effects; theoretical exploration and logical organization of a number of self sustaining yet pivotal matters up to the mark layout as they pertain to switched linear structures: controllability and observability, suggestions stabilization, optimization and periodic switching; a competent beginning for additional theoretical learn in addition to layout information for genuine lifestyles engineering functions during the integration of novel principles, clean insights and rigorous effects.
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Additional info for Switched Linear Systems: Control and Design (Communications and Control Engineering)
Example text
Let Sτ be the set of switching signals with dwell-time τ . It is clear that any switching signal with a positive dwell time is well-defined. The converse is not necessarily to be true, for instance, the switching path θ(t) = 1 2 if t ∈ [k − k1 , k + k1 ) for some k ∈ N+ otherwise is completely well-defined over [0, ∞), but it does not permit a positive dwell time. 5 Solutions of Switched Linear Systems For a nonlinear system, usually it is very hard (if not impossible) to explicitly express the solution in terms of the system parameters in an analytic way.
T. t. t. the switching signal. Given a switched system, if the switching signal is a switching path or a time-driven switching law, the well-posedness of the switched system and the well-definedness of the switching signal are decoupled and hence are independent of each other. However, for a switching signal in the event-driven form, its well-definedness implies that the state information is available on [t0 , t1 ), which means that the switched system admits at least one solution at x0 over [t0 , t1 ).
T+) = ψ (σ(t), y(t), z(t)) . t. the switched system, if there is a state trajectory x : [t0 , t1 ) → Rn with x(t0 ) = x0 , such that for almost any t ∈ [t0 , t1 ), we have 18 1 Introduction δx(t) = fθ(t) (x(t), u(t)) y(t) = hθ(t) (x(t)) θ(t+) = ψ (θ(t), x(t)/y(t), z(t)) . t. different switched systems. , σ(t+) = ψ (x(t)) . , σ(t+) = ψ (y(t)) . 21) A typical pure-state-feedback switching law is the quadratic form σ(t+) = arg min{xT (t)P1 x(t), · · · , xT (t)Pm x(t)} where Pi , i ∈ M are real matrices.