Stability Theory of Switched Dynamical Systems by Zhendong Sun

By Zhendong Sun

Stability concerns are basic within the examine of the various advanced nonlinear dynamic behaviours inside switched structures. Professors solar and Ge current an intensive research of balance results on 3 extensive sessions of switching mechanism:

• arbitrary switching the place balance represents robustness to unpredictable and bad perturbation;

• limited switching, together with random (within a recognized stochastic distribution), dwell-time (with a recognized minimal length for every subsystem) and autonomously-generated (with a pre-assigned mechanism) switching; and

• designed switching during which a measurable and freely-assigned switching mechanism contributes to balance via performing as a keep an eye on enter.

For each one of those periods Stability conception for Switched Dynamical Systems propounds:

• specified balance research and/or layout;

• comparable robustness and function concerns;

• connections to different recognized keep an eye on difficulties; and

• many motivating and illustrative examples.

Academic researchers and engineers drawn to structures and keep watch over will locate this ebook of serious price in facing all types of switching and it'll be an invaluable resource of complementary studying for graduate scholars of nonlinear platforms theory.

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Additional resources for Stability Theory of Switched Dynamical Systems

Example text

As a result, V is globally Lipschitz continuous. It is obvious that V is 0-symmetric, and positively homogeneous of degree one. Thus, it is indeed a norm. 21, a stable (marginally stable) switched system always admits a norm as its common (weak) Lyapunov function. 28). It is clear that any continuoustime switched linear system is regular and that a discrete-time system is regular if (A) = −∞. For a continuous-time switched linear system A = {A1 , . . , Am }, the normalized switched system is the switched system A = {A1 − (A)In , .

With the help of the sum-of-squares technique, we present a homogeneous polynomial Lyapunov function approach for calculating an upper bound of the least stable dwell time. For dwell-time stabilizability, the concept of -robust dwell time is introduced to keep a balance between the quality of the switching signal and the performance of the continuous state. A new combined switching strategy is also developed to further enlarge the dwell time without deteriorating the system performance. The object of Chap.

38 2 Arbitrary Switching Conversely, suppose that the switched system admits an extreme norm · with A = LNA = 1. It is clear that the system is either stable or marginally stable. If the system is stable, then, there is a common Lyapunov norm V0 such that V0 (Ai x) − V0 (x) ≤ −ω(x) ∀x ∈ Rn , i ∈ M, where ω is a continuous positive definite function. Let β = minV0 (x)=1 ω(x). It follows that V0 (Ai x) − V0 (x) ≤ −βV0 (x) ∀x ∈ Rn , i ∈ M, which further implies that A V0 ≤ 1 − β, a contradiction. Therefore, the switched system must be marginally stable.

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