Ensemble Feedback Stabilization of Linear Systems

This paper is concerned with feedback stabilization of linear systems with multiple delays. Based on an integral performance of the state transition matrix of the linear delay systems, a numerical optimization algorithm is presented to seek feedback gain matrices to stabilize the delay systems. The effectiveness of the algorithm is interpreted by a theoretical result and numerical examples.

This paper is concerned with the nonlinear static state feedback stabilization of time-invariant linear multivariable continuous-time systems with friction driven backlash in the control inputs. A time-invariant static nonlinear state feedback compensator is proposed, easily obtainable solving an algebraic Riccati equation. The global asymptotic stability of the resulting closed-loop nonlinear system is proved using the Lyapunov's direct method and the La Salle's invariance principle. A simulation study shows that the proposed nonlinear state feedback compensator achieves an overall stabilization performance significantly better than the known backlash inverse compensator.

Output feedback stabilization of linear systems with delayed input

Numerical optimization for feedback stabilization of linear systems with distributed delays

The problem of output feedback stabilization of linear systems with a singular perturbation model is addressed in this paper. A design method based on an accurate reduced-order model is proposed for this kind of system. This approach can overcome the difficulties in the existing design method using the so-called zero-order approximation model, whose validity is highly dependent on the value of the perturbation parameter. The closed-loop stability of the design method is analyzed and robust stability condition is given.

This article considers the memoryless feedback stabilization of linear systems with unknown input delay. In order to accomplish this problem, we focus on systems without exponentially unstable poles, and by using the truncated predictor feedback (TPF) design technique, we propose a finite-dimensional control scheme to avoid the implementation problems that arise in typical infinite-dimensional control schemes. When the unknown delay is limited, the devised memoryless TPF controller can achieve global stabilization of the closed system. In the end, we verify the effectiveness of the control scheme with numerical example.

The efficacy of nonlinear control in the quadratic stabilization of linear systems containing norm bounded uncertainty is considered. In particular, the author examines the quadratic stabilization of uncertain systems via dynamic output feedback control. It is conjectured that, if a linear system containing norm bounded uncertainty can be stabilized via nonlinear control, then it can also be stabilized using linear control. The main result of this work proves this conjecture for a class of uncertain systems containing a single scalar uncertain parameter. >

On the fixed-time stabilization of input delay systems using act-and-wait control

Pseudo-predictor feedback stabilization of linear systems with time-varying input delays

This paper is concerned with stabilization of (time-varying) linear systems with a single time-varying input delay by using the predictor based delay compensation approach. Differently from the traditional predictor feedback which uses the open-loop system dynamics to predict the future state and will result in an infinite dimensional controller, we propose in this paper a pseudo-predictor feedback (PPF) approach which uses the (artificial) closed-loop system dynamics to predict the future state and the resulting controller is finite dimensional and is thus easy to implement. Necessary and sufficient conditions guaranteeing the stability of the closed-loop system under the PPF are obtained in terms of the stability of a class of integral delay operators (systems). Moreover, it is shown that the PPF can compensate arbitrarily large yet bounded input delays provided the open-loop (time-varying linear) system is only polynomially unstable and the feedback gain is well designed. Comparison of the proposed PPF approach with the existing results are well explored. Numerical examples demonstrate the effectiveness of the proposed approaches.

This paper is concerned with stabilization of linear systems with both input delay and state delay, by utilizing the predictor based delay compensation method. The future dynamics of system are predicted by the proposed pseudo predictor feedback (PPF) control scheme. It is proved that the stability of the time-delay system under the PPF controller is equivalent to the stability of a corresponding integral delay system. The proposed method is also adopted for the stabilization of time-varying time-delay systems. A numerical example is carried out to illustrate the effectiveness of the proposed approach.

This article focuses on the dual-observer-based stabilization of linear systems with delays in both the inputs and outputs. By a model reduction approach the system can be converted to an equivalent linear system without delays, for which a dual-observer-based stabilizing controller can be designed. However, such a controller is infinite dimensional or memory-based. To solve such a problem, a modified memoryless dual-observer-based stabilizing controller is designed, and the closed-loop stability is proven under some additional conditions. Compared with the reduced-order observer-based controller, the dimension of the dual-observer-based controller is smaller if the system has more inputs than outputs. At the same time, the design approach is more challenging in proving closed-loop stability, as for example a more intricate Lyapunov-Krasovskii functional has to be constructed associated with the proposed approach. The proposed approach is applicable to both continuous-time and discrete-time systems. Numerical simulations validate the effectiveness of the proposed method.

Observer-based feedback stabilization of linear systems with event-triggered sampling and dynamic quantization

This paper investigates the feedback stabilization problem for SISO linear uncertain control systems with saturating quantized measurements. In the fixed quantization sensitivity framework, we propose a time varying control law able to effectively account for the presence of saturation, which is often the main source of instability, designed using sliding mode techniques. Such controller is proved able to stabilize the plant both in the presence and in the absence of quantization.

This paper addresses feedback stabilization problems for linear time-invariant control systems with saturating quantized measurements. We propose a new control design methodology, which relies on the possibility of changing the sensitivity of the quantizer while the system evolves. The equation that describes the evolution of the sensitivity with time (discrete rather than continuous in most cases) is interconnected with the given system (either continuous or discrete), resulting in a hybrid system. When applied to systems that are stabilizable by linear time-invariant feedback, this approach yields global asymptotic stability.