Observer-based H∞ finite-time controller for time-delay nonlinear one-sided Lipschitz systems with exogenous disturbances

Abstract

This paper is concerned with a robust observer-based control of nonlinear one-sided Lipschitz systems in the presence of time delay, model uncertainties, and unknown energy-bounded exogenous disturbances. In this regard, firstly, an appropriate observer is designed and then a controller is achieved based on estimated state variables. Considering dynamical equations of the system together with dynamical equations of the observer error, the sufficient conditions are given for robust finite-time boundedness of the closed-loop system and satisfying the H∞ performance index. In this regard, a theorem is given and the sufficient conditions are derived in terms of feasibility testing of given linear matrix inequalities by selecting an appropriate Lyapunov–Krasovskii functional. Finally, computer simulations are performed for two examples to show the efficiency and applicability of the proposed controller.

Separation principle for quasi‐one‐sided Lipschitz nonlinear systems with time delay

“…In addition, time‐delays pose a challenging issue not only in observers design problem but also in controller design theory. The topic of stability of nonlinear time‐delay systems has received huge attention in the past decade …”

“…In Reference , an output feedback control method with prescribed performance is proposed for single‐input and single‐output switched nonstrict‐feedback nonlinear systems, which is assumed that nonlinear functions of the concerned systems are unknown, switching signals are unknown and arbitrary, and the states are unmeasured. In Reference , a robust observer‐based control of nonlinear one‐sided Lipschitz systems in the presence of time delay, model uncertainties, and unknown energy‐bounded exogenous disturbances is concerned. In Reference , the control design problem for stochastic one‐sided Lipschitz differential inclusion system with time delay is considered.…”

“…The topic of stability of nonlinear time-delay systems has received huge attention in the past decade. [18][19][20][21][22][23][24] In Reference 18, a delay-range-dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time-delay systems under input saturation is described. An adaptive output-feedback neural network control scheme for a class of stochastic nonlinear time-varying delay systems with unknown control directions is presented in Reference 19.…”

Sustained oscillations in MIMO nonlinear systems through limit cycle shaping

“…Such systems include an important class of dynamic systems, for example, multilink robots and quadrotors . In literature, different procedures have been developed for solving the regulation or tracking problems in MIMO nonlinear systems . So far, there is no result on stable limit cycle shaping for MIMO nonlinear systems.…”

“…[23][24][25] In literature, different procedures have been developed for solving the regulation or tracking problems in MIMO nonlinear systems. 23,[26][27][28][29] So far, there is no result on stable limit cycle shaping for MIMO nonlinear systems.In this paper, the limit-cycle shaping problem of MIMO nonlinear systems is considered. The MIMO system includes some subsystems.…”