Class Of Triangular Nonlinear Systems Research Articles

Prescribed-Time Sliding Mode Observer for Nonlinear Triangular Systems

This paper deals with the problem of prescribed-time sliding mode observer design for a class of triangular nonlinear systems. The contribution of the paper is twofold. First, we propose a new prescribed-time observer based on Super-Twisting-Algorithm (STA), for a triangular two-dimensional system. Such an STA algorithm is based on the use of two power terms, instead of only one as with the standard STA. Then we exploit this algorithm to develop a novel step-by-step arbitrary order sliding mode observer for a general class of triangular systems. An application to vehicle motion estimation in a platoon is provided to show the validity and efficiency of the proposed step-by-step sliding mode observer. For this case study, we use a third-order longitudinal kinematic linear vehicle model.

Practical prescribed-time sampled-data control of triangular nonlinear systems satisfying a linear growth condition by linear time-varying feedback

In this paper, the practical prescribed-time sampled-data control problem of a class of triangular nonlinear systems satisfying a linear growth condition is studied. With the help of some properties of a class of parametric Lyapunov equations (PLEs) and by constructing a time-varying Lyapunov-like function, a linear time-varying feedback controller is designed to make the states of the closed-loop system converge to an arbitrarily small neighbourhood of the origin in any prescribed time, while the control siginals are guaranteed to be bounded. A numerical example validates the effectiveness of the proposed method.

Cascade high-gain observers for a class of nonlinear systems with large delayed measurements

ABSTRACTThis paper proposes a cascade high-gain observer for a class of triangular nonlinear systems with large and diverse time delays at states and output equation. Compared with some existing results in the literature, the main contribution is to consider the simultaneous and diverse delays in both states and output and further, to propose a cascade observer in dealing with arbitrarily large delayed measurements. By choosing a suitable Lyapunov-Krasovskii functional, the sufficient condition is presented that guarantees the exponential convergence of observation error to the origin. Simulation results on a numerical example and a practical case study involving inverted pendulum are finally given to illustrate the effectiveness of the proposed approach.

Continuous Sampled-Data Observer Design for Nonlinear Systems With Time Delay Larger or Smaller Than the Sampling Period

This technical note addresses the problem of high gain observer design for a class of triangular nonlinear systems with sampled and delayed output measurements. The transmission delay may be larger or smaller than the sampling period. Firstly, a class of hybrid systems are introduced, and sufficient conditions are proposed to guarantee that the hybrid systems are globally and exponentially stable. Then, a continuous-discrete observer is designed for the nonlinear systems. Based on these sufficient conditions and a specially constructed Lyapunov-Krasovskii functional, it is shown that the observation errors globally and exponentially converge to the origin. Finally, an illustrative example is used to verify the validity of the proposed design methods.

Sampled-data chain-observer design for a class of delayed nonlinear systems

ABSTRACTThe problem of observer design is addressed for a class of triangular nonlinear systems with not-necessarily small delay and sampled output measurements. One more difficulty is that the system state matrix is dependent on the un-delayed output signal which is not accessible to measurement, making existing observers inapplicable. A new chain observer, composed of m elementary observers in series, is designed to compensate for output sampling and arbitrary large delays. The larger the time-delay the larger the number m. Each elementary observer includes an output predictor that is conceived to compensate for the effects of output sampling and a fractional delay. The predictors are defined by first-order ordinary differential equations (ODEs) much simpler than those of existing predictors which involve both output and state predictors. Using a small gain type analysis, sufficient conditions for the observer to be exponentially convergent are established in terms of the minimal number m of elementary observers and the maximum sampling interval.

Output-feedback sliding-mode control via cascade observers for global stabilisation of a class of nonlinear systems with output time delay

This article proposes a sliding-mode control scheme for a class of triangular nonlinear systems with arbitrarily long and known time delay in the output signal. The proposed control strategy guarantees global asymptotic stability of the closed-loop system using only output feedback, without using any kind of approximations. The state of the system is estimated by asymptotic observers connected in cascade. The analysis of such observers in closed-loop feedback is also a contribution of the present manuscript as well as the theoretical demonstration of the chattering elimination even in the presence of delays. Simulation results and a physically motivated example with a full-bridge power converter illustrate the effectiveness of the proposed approach.

An explicit formula of bounded feedback stabilizers for feedforward systems

This work constitutes continuation of a recent result of the same authors, which provides an explicit formula for bounded feedback stabilizers for a wide class of triangular nonlinear systems. In the present paper the previous result is extended for nonlinear systems having feedforward structure and whose linearization at the equilibrium is in general uncontrollable.