Decentralized sliding mode quantized feedback control for a class of uncertain large-scale systems with dead-zone input

Abstract

This paper is concerned with the robust quantized feedback stabilization problem for a class of uncertain nonlinear large-scale systems with dead-zone nonlinearity in actuator devices. It is assumed that state signals of each subsystem are quantized and the quantized state signals are transmitted over a digital channel to the controller side. Combined with a proposed discrete on-line adjustment policy of quantization parameters, a decentralized sliding mode quantized feedback control scheme is developed to tackle parameter uncertainties and dead-zone input nonlinearity simultaneously, and ensure that the system trajectory of each subsystem converges to the corresponding desired sliding manifold. Finally, an example is given to verify the validity of the theoretical result.

Appendix: Proof of the technical lemma

Proof of Lemma 2

First, it is obvious that the inequality

(22)

is satisfied by virtue of (5). Next, we will illustrate that the inequality $|C_{i}|\varDelta _{i}\mu_{i}\leq\frac{1}{\beta_{i}}|C_{i}q_{\mu_{i}}(x_{i})|$ holds when the parameter μ _i satisfies $0<\mu_{i}\leq\frac{|C_{i}x_{i}|}{(\beta_{i}+1)|C_{i}|\varDelta _{i}}$.

Multiplying (β _i +1)|C _i |Δ _i from both sides of (8), we have

(23)

Subtracting |C _i |Δ _i μ _i from both sides of the above inequality (23), one can obtain

Furthermore, combined with inequality (22), it is easy to check that

Owing to the triangle basic inequality |a−b|≥|a|−|b|,∀a∈ℝ,b∈ℝ, it follows that

Utilizing the relationship $q_{\mu_{i}}(x_{i})=x_{i}+e_{\mu_{i}}$, one can see that

(24)

Therefore, by virtue of (22) and (24), it can be seen that (9) is obtained. Thus, the proof is completed. □