Abstract
This paper considers the problem ofH∞output tracking control for discrete-time switched systems with time-varying delay and external disturbances. The control scheme combining disturbance observer-based control (DOBC) andH∞control is proposed. The disturbances are assumed to include two parts. One part is generated by an exogenous system, which imposes on system with control inputs in the same channel. The other part is supposed to have the boundedH2norm. A new disturbance observer is developed to estimate and reject the first case disturbances for switched system with time-varying delay, and the second case disturbances are attenuated byH∞control scheme. The stability analysis of the closed-loop system is developed by switched Lyapunov function, and a solvable delay-dependent sufficient condition is presented in terms of linear matrix inequalities (LMIs) and cone complement linearization (CCL) methods. A numerical example is given to demonstrate the effectiveness of the proposed composite control scheme.
Highlights
Switched systems are a special class of hybrid control systems, which are composed of a family of subsystems described by continuous or discrete time dynamics and a switched rule among them [1, 2]
Mathematical Problems in Engineering control (DOBC) scheme has been studied from 1980s and applied in many control fields [26,27,28,29,30,31,32,33,34,35,36,37], which can be regarded as an active disturbance rejection method
Where d1(k) is the estimation of the disturbances d1(k), which is obtained by the following disturbance observer: ω (k) = ] (k) − Lx (k)
Summary
Switched systems are a special class of hybrid control systems, which are composed of a family of subsystems described by continuous or discrete time dynamics and a switched rule among them [1, 2]. Mathematical Problems in Engineering control (DOBC) scheme has been studied from 1980s and applied in many control fields [26,27,28,29,30,31,32,33,34,35,36,37], which can be regarded as an active disturbance rejection method. Exponential l2 − l∞ output tracking control problem has been solved in [13] for a class of discrete-time switched systems. A composite control scheme is developed to solve the problem of H∞ output tracking control for discrete-time switched systems with time-varying delay and external disturbances. A numerical example is provided to demonstrate the effectiveness of the main result
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