This article investigates the stochastic stability of stochastic differential delay systems (SDDSs) with path information and their applications in consensus control of multi-agent systems (MASs) based on the path information feedback. Here, the integral path information and fragment-integral path information are considered respectively. The mean square (m.s.) and almost sure (a.s.) exponential stability criteria of the SDDSs with path integral information are established respectively according to the two types of path information. It is shown that the fragment-integral term may work positively for stochastic stability. Moreover, the obtained stochastic stability theorems are applied to design a distributed proportional integral/ fragment-integral control protocol and establish consensus conditions for stochastic MASs under proportional-integral (PI) -type controls. Finally, the effectiveness of the results is verified through two simulation examples.

Real-world dynamical control systems are often subject to input saturation due to the physical constraints of actuators. This causes the response performance of the system to be reduced due to the effect of input saturation. To this end, we propose a finite-time performance enhanced bounded control (FTPE-BC) method based on sliding mode control for finite time tracking of linear systems with input saturation. In this method, an approach rate based on inverse tangent function is proposed to make the system converge in finite time. A bounded controller based on sliding mode control is proposed, in which two control parameters are introduced to reduce steady-state error, settling time and overshoot. Meanwhile, the finite-time stability of the system is proved in a domain of attraction. The parameters selection principle of the controller is given to improve the transient and steady-state performance of the closed-loop system. The simulation results verify the superiority of the proposed method in the transient and steady-state performance enhancement.

This work is absorbed in the neighboring mode-dependent event-triggered control scheme for Markov jump systems with unknown interconnections. A dynamic event-triggered mechanism composed of neighboring modes parameters is provided to save communication resources and reduce the number of solution parameters. Distinguished from existing version, the global operating modes are required to be unknown for each local subsystem. Resorting to neighboring modes information, an event-triggered state feedback controller is established to assure system stability. The cyclic-small-gain criterion is used to tackle the unknown interconnections so that novel stability criteria are obtained for the closed-loop systems with H ∞ performance. Finally, an illustrative example is employed to confirm the proposed method in the aspect of validity.

This paper is concerned with parameter estimate and adaptive control problems of deterministic autoregressive moving average (DARMA) systems on the basis of quantized data of system output signals which are generated by a kind of uniform quantizer. By designing system input signals, the extended least-squares (ELS) algorithm with uniform output observations is proved to yield bounded estimation errors under some mild assumptions. Moreover, the adaptive tracking controller under inaccuracy observations are also designed. To analyse the properties of tracking error, I use the expanded form of ELS and research the properties of quantization noise. In addition, I give the expression of tracking error and show how it depends on the size of quantization step when the quantization step satisfies some conditions. A numerical example is supplied to demonstrate the theoretical results.

Monte Carlo simulations have long been a widely used method in the industry for control system validation. They provide an accurate probability measure for sufficiently frequent phenomena, but are often time-consuming and may fail to detect very rare events. Conversely, deterministic techniques such as µ or IQC-based analysis allow fast calculation of worst-case stability margins and performance levels, but in the absence of a probabilistic framework, a control system may be invalidated on the basis of extremely rare events. Probabilistic µ-analysis has therefore been studied since the 1990s to bridge this analysis gap by focusing on rare but nonetheless possible situations that may threaten system integrity. The solution adopted in this paper implements a branch-and-bound algorithm to explore the whole uncertainty domain by dividing it into smaller and smaller subsets. At each step, sufficient conditions involving µ upper bound computations are used to check whether a given requirement – related to the delay margin in the present case – is satisfied or violated on the whole considered subset. Guaranteed bounds on the exact probability of delay margin satisfaction or violation are then obtained, based on the probability distributions of the uncertain parameters. The difficulty here arises from the exponential term classically used to represent a delay, which must be replaced by a rational expression to fit into the Linear Fractional Representation (LFR) framework imposed by µ-analysis. Two different approaches are proposed and compared in this paper. First, an equivalent representation using a rational function of degree 2 with the same gain and phase as the real delay, which results into an LFR with frequency-dependent uncertainty bounds. Then, a Padé approximation, whose order should be chosen carefully to handle the trade-off between conservatism and complexity. A constructive way to derive minimal LFR from Padé approximations of any order is also provided as an additional contribution. The whole method is first assessed on a simple satellite benchmark, and its applicability to realistic problems involving a larger number of states and uncertainties is then demonstrated.

Steering a nonlinear system from one state to a desired one is a common task in control. While a nominal trajectory can be obtained rather systematically using a model, for example via numerical optimization, heuristics, or reinforcement learning, the design of a computationally fast and reliable feedback control law that guarantees robust asymptotic stability of the found trajectory can be much more involved. An approach that does not require high online computational power and is well-accepted in the industry is gain-scheduling. The results presented here pertain to the stability guarantees and the region of attraction of gain scheduled control laws, based on subsequent linearizations along the reference trajectory. The approach bounds the uncertainty arising from the linearization process, builds polytopic sets of linear time varying systems covering the nonlinear dynamics along the trajectory, and exploits sufficient conditions for robust stability to attempt the derivation of the desired gain-scheduled controller, via the solution of Linear Matrix Inequalities (LMIs). A result to estimate an ellipsoidal region of attraction is provided too. Moreover, arbitrary scheduling strategies between the control gains are considered in the analysis, and the method can be used also to check/assess the stability properties obtained with an existing gain-scheduled law. The approach is demonstrated experimentally on a small quadcopter as well as in simulation to design a scheduled controller for a chemical reactor model and to validate an existing control law for a gantry crane model.