Stabilization of Switched Nonlinear Systems with Unstable by Hao Yang

By Hao Yang

This ebook offers its reader with a great knowing of the stabilization of switched nonlinear structures (SNS), structures which are of useful use in diversified events: layout of fault-tolerant platforms in house- and plane; site visitors regulate; and warmth propagation regulate of semiconductor energy chips. the sensible historical past is emphasised during the booklet; attention-grabbing functional examples usually illustrate the theoretical effects with plane and spacecraft given specific prominence.

Stabilization of Switched Nonlinear structures with volatile Modes treats numerous diverse subclasses of SNS in line with the features of the person approach (time-varying and allotted parameters, for example), the kingdom composition of person modes and the measure and distribution of instability in its quite a few modes. fulfillment and upkeep of balance around the procedure as a complete is reinforced by means of buying and selling off among person modes that could be both good or volatile or by way of exploiting components of partial balance inside the entire volatile modes.

The publication can be utilized as a reference for tutorial examine on switched structures or utilized by graduate scholars of keep an eye on thought and engineering. Readers must have studied linear and nonlinear procedure thought and feature a few wisdom of switched and hybrid platforms to get the main from this monograph.

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Extra resources for Stabilization of Switched Nonlinear Systems with Unstable Modes

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We consider the worst case that Ω (t N −2 ) = ι. The results for other cases are obtained straightforwardly. 34) that u = u i , f ∈ Fi =⇒ Vi (x(t)) ≤ e−λ0 (t−t0 ) Vi (x(t0 )) u = u i , f ∈ F j , j = i =⇒ Vi (x(t)) ≤ eλ1 (t−t0 ) Vi (x(t0 )) . 38) 30 2 Switched Nonlinear Systems with Partial Unstable Modes Fig. 8 Activating periods of different controllers long enough short enough ... 38), we further have Vι (x(t)) ≤ μ0 e−λ0 (t−t N −2 ) VΩ (t − N −2 ) (x(t N −2 )) ≤ μ20 e−λ0 (t−t N −2 ) eλ1 τ VΩ (t − N −3 ) (x(t N −3 )) ..

Let u r = Dr u¯ r where u¯ r ∈ 3 = [u¯ r 1 , u¯ r 2 , u¯ r 3 ]∅ is the output of the control processor, Dr = diag[Dr 1 , Dr 2 , Dr 3 ] with Dri = 1 i = 1, 2, 3 denotes the actuator gain matrix. Also let u p = D p u¯ p where u¯ p ∈ N = [u¯ p1 , . . , u¯ pN ]∅ is the output of the control processor, D p = diag[D p1 , . . , D pN ] with D pi = 1 i = 1, . . , N denotes the piezoelectric actuator gain matrix. Under I , u r and u p become zero. , let Dri = 0, D pi = 0, such an operation is available since both thrusters and piezoelectric actuators can work in both continuous and impulsive ways.

Denote γ = η˙ + δω, define a new state variable ψ = (η∅ γ ∅ )∅ . 53) where υ −J0−1 ω× (J0 ω+δ(ψ −δω))+δ ∅ (K C)ψ −(δ ∅ Cδ+ω× δ ∅ δ)ω+δ ∅ δ2 u p with J0 J − δ ∅ δ. Now we consider the model of faults. Let u r = Dr u¯ r where u¯ r ∈ 3 = [u¯ r 1 , u¯ r 2 , u¯ r 3 ]∅ is the output of the control processor, Dr = diag[Dr 1 , Dr 2 , Dr 3 ] with Dri = 1 i = 1, 2, 3 denotes the actuator gain matrix. Also let u p = D p u¯ p where u¯ p ∈ N = [u¯ p1 , . . , u¯ pN ]∅ is the output of the control processor, D p = diag[D p1 , .

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