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This paper investigates the control synthesis for discrete-time semi-Markov jump systems with nonlinear input. Observer-based controllers are designed in this paper to achieve a better performance and robustness. The nonlinear input caused by actuator saturation is considered as a group of linear controllers in the convex hull. Moreover, the elapse time and mode dependent Lyapunov functions are investigated and sufficient conditions are derived to guarantee the H∞ performance index. The largest domain of attraction is estimated as the existing saturation in the system. Finally, a numerical example is utilized to verify the effectiveness and feasibility of the developed strategy. [ABSTRACT FROM AUTHOR]

We propose a novel method for constructing probabilistic robust disturbance rejection control for uncertain systems in which a scenario optimization method is used to deal with the nonlinear and unbounded uncertainties. For anti-disturbance, a reduced order disturbance observer is considered and a state-feedback controller is designed. Sufficient conditions are presented to ensure that the resulting closed-loop system is stable and a prescribed H∞ performance index is satisfied. A numerical example is presented to illustrate the effectiveness of the techniques proposed and analyzed. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of probabilistic robust stabilization for uncertain systems subject to input saturation. A new probabilistic solution framework for robust control analysis and synthesis problems is addressed by a scenario optimization approach, in which the uncertainties are not assumed to be norm bounded. Furthermore, by expressing the saturated linear feedback law on a convex hull of a group of auxiliary linear feedback laws, we establish conditions under which the closed-loop system is probabilistic stable. Based on these conditions, the problem of designing the state feedback gains for achieving the largest size of the domain of attraction is formulated and solved as a constrained optimization problem with linear matrix inequality constraints. The results are then illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of robust stabilization for uncertain systems subject to input saturation and nonhomogeneous Markovian jumps, where the uncertainties are assumed to be norm bounded and the transition probabilities are time-varying and unknown. By expressing the saturated linear feedback law on a convex hull of a group of auxiliary linear feedback laws and the time-varying transition probabilities inside a polytope, we establish conditions under which the closed-loop system is asymptotically stable. On the basis of these conditions, the problem of designing the state feedback gains for achieving fast transience response with a guaranteed size of the domain of attraction is formulated and solved as a constrained optimization problem with linear matrix inequality constraints. The results are then illustrated by numerical examples including the application to a DC motor speed control example. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of robustL2−L∞filtering for a class of dynamical systems with nonhomogeneous Markov jump process. The time-varying transition probabilities which evolve as a nonhomogeneous jump process are described by a polytope, and parameter-dependent and mode-dependent Lyapunov function is constructed for such system, and then a robustL2−L∞filter is designed which guarantees that the resulting error dynamic system is robustly stochastically stable and satisfies a prescribedL2−L∞performance index. A numerical example is given to illustrate the effectiveness of the developed techniques. [ABSTRACT FROM PUBLISHER]

The problem of robust fault detection (RFD) is studied for a class of discrete‐time stochastic systems with non‐homogeneous jump processes. First, a filter‐based residual signal generator is constructed. To guarantee the sensitivity to faults and robustness against unknown inputs, both H∞ performance and a new performance index are considered. Then an FD filter, which minimises the influences of the disturbances, modelling uncertainties and increases the sensitivity to faults, is designed. A sufficient condition for ensuring the existence of RFD filter in terms of linear‐matrix inequalities is established. A simulation is carried out, illustrating that the proposed RFD filter can detect the faults after their occurrences in a timely manner. [ABSTRACT FROM AUTHOR]

This paper studies the problem of continuous gain-scheduled robust fault detection (RFD) on a class of time-delay stochastic nonlinear systems with partially known jump rates. By means of gradient linearization procedure, stochastic linear models and filter-based residual signal generators are constructed in the vicinity of selected operating states. Furthermore, in order to guarantee the sensitivity to faults and robustness against unknown inputs, an RFD filter (RFDF) is designed for such linear models by first designing H\infty filters that minimize the influences of the disturbances and modeling uncertainties and then a new performance index that increases the sensitivity to faults. Subsequently, a sufficient condition on the existence of RFDF is established in terms of linear matrix inequality techniques. Finally, a continuous gain-scheduled approach is employed to design continuous RFDFs on the entire nonlinear jump system. A simulation example is given to illustrate that the proposed RFDF can detect the faults correctly and shortly after the occurrences. [ABSTRACT FROM AUTHOR]