scholarly journals H∞Control for Stochastic Systems with Markovian Switching and Time-Varying Delay via Sliding Mode Design

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Lijun Gao ◽  
Yuqiang Wu
Keyword(s):  
Stochastic Systems ◽  
Sliding Mode ◽  
Nonlinear Function ◽  
Markovian Switching ◽  
Time Varying ◽  
Sliding Surface ◽  
Parameter Uncertainties ◽  
Time Varying Delay ◽  
Integral Sliding Surface ◽  
The Given

This paper addresses the problem ofH∞control for a class of uncertain stochastic systems with Markovian switching and time-varying delays. The system under consideration is subject to time-varying norm-bounded parameter uncertainties and an unknown nonlinear function in the state. An integral sliding surface corresponding to every mode is first constructed, and the given sliding mode controller concerning the transition rates of modes can deal with the effect of Markovian switching. The synthesized sliding mode control law ensures the reachability of the sliding surface for corresponding subsystems and the global stochastic stability of the sliding mode dynamics. A simulation example is presented to illustrate the proposed method.

Sliding Mode Control Based on Novel Nonlinear Sliding Surface for a Class of Time-Varying Delay Systems

2014 ◽  
Vol 615 ◽  
pp. 375-381
Author(s):  
Qi Feng Ren ◽  
Cun Che Gao ◽  
Shu Hui Bi
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Sliding Surface ◽  
Time Varying Delay ◽  
Mode Control ◽  
Varying Delay

The sliding mode control (SMC) design is discussed for a class of time-varying delay systems which is delay-range-dependent and rate-range-dependent. A novel time-varying nonlinear sliding surface is employed. The choice of nonlinear sliding surface is to change the state matrix of sliding mode system, which can combine the advantages of different conventional linear sliding surfaces. Thus the better transient qualities of system states, i.e., quicker response and smaller overshoot, can be achieved. The sufficient conditions ensuring the asymptotic stability of sliding mode are derived in terms of linear matrix inequalities. The algorithms deciding unknown parameters of the nonlinear sliding surface and the corresponding sliding mode controller are also presented. Finally, A numerical example is given to illustrate the effectiveness of the result here.

Sign in / Sign up

Export Citation Format

Share Document