An Observer-Based Output Feedback Controller for the Finite-Time Stabilization of Markov Jump Linear Systems

The finite‐time stability (FTS) of a symmetrically interconnected system is studied under the consideration of utilizing the system structural properties to reduce the complexity of analysis. The FTS of this kind of large‐scale system can be guaranteed by that of two lower dimensional systems. The concept of mixed stability, taking care of both transient and steady‐state performances of a system, is introduced. Based on the FTS analysis, a decentralized finite‐time controller via state feedback is given to stabilize the large‐scale system. Meanwhile, an observer‐based decentralized output feedback controller is provided to make the closed‐loop system finite‐time stable. The FTS conditions and related decentralized stabilization controller parameters are both derived from solving some differential or algebraic linear matrix inequalities.

A problem of designing an output feedback controller to improve transient performance in uncertain linear time-varying systems subjected to bounded external disturbances is considered. For systems with the dynamics specified by polytopic uncertainties, we design linear reduced-order dynamic controllers to bound the system state trajectories below a specified threshold over a predefined finite time interval. Using the notion of dissipativity, we also ensure that the system is robust with respect to bounded external disturbances over the finite time interval. Sufficient conditions for the uncertain closed-loop system trajectories to simultaneously satisfy finite-time boundedness and dissipativity to external disturbances are given in terms of parameter-dependent differential matrix inequalities. Further, parameter-independent differential linear matrix inequality (DLMI) conditions are presented to design time-varying control gains. The proposed dissipativity-based approach is less conservative as it generalises the procedure of designing finite-time robust controllers, encompassing various disturbance attenuation performance criteria like passivity and finite L 2 -gain. The applicability of the proposed approach is demonstrated through numerical simulation examples.

This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs) and linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed methodology.

Finite time stability and stabilization of hybrid dynamic systems

This technical note is concerned about the finite-time stability and stabilization for Ito stochastic systems with Markovian switching. A mode-dependent parameter approach is proposed to give a sufficient condition for finite-time stability, and its superiority to common parameter approach is analyzed. Moreover, the finite-time stabilization is studied and two new sufficient conditions for the existence of state and output feedback controllers are presented in terms of coupled matrix inequalities. A N-mode algorithm is given for solving the obtained matrix inequalities arising from finite-time stability(stabilization). Finally, an example is employed to illustrate the effectiveness of our obtained results.

Differential Linear Matrix Inequalities in Optimal and Robust Sampled-Data Filtering

In this study, the problem of finite-time stability and boundedness for parabolic singular distributed parameter systems in the sense of [Formula: see text] norm is investigated. First, two new results on [Formula: see text] norm-based finite-time stability and finite-time boundedness for above-mentioned systems, inspired by the light of partial differential equations theory and Lyapunov functional method, are presented. Then, some sufficient conditions of [Formula: see text] norm-based finite-time stability and boundedness are established by virtue of differential inequalities and linear matrix inequalities. Furthermore, the distributed state feedback controllers are constructed to guarantee the [Formula: see text] norm-based finite-time stable and bounded of the closed-loop singular distributed parameter systems. Finally, numerical simulations on a specific numerical example and the building temperature control system equipped with air conditioning are given to demonstrate the validity of the proposed methods.

Finite-time output-feedback synchronization control for bilateral teleoperation system via neural networks

Sampled-data control of Lur’e systems

This paper presents a funnel synthesis algorithm for computing controlled invariant sets and feedback control gains around a given nominal trajectory for dynamical systems with locally Lipschitz nonlinearities and bounded disturbances. The resulting funnel synthesis problem involves a differential linear matrix inequality (DLMI) whose solution satisfies a Lyapunov condition that implies invariance and attractivity properties. Due to these properties, the proposed method can balance maximization of initial invariant funnel size, i.e., size of the funnel entry, and minimization of the size of the attractive funnel for attenuating the effect of disturbance. To solve the resulting funnel synthesis problem with the DLMI as constraints, we employ a numerical optimal control approach that uses a multiple shooting method to convert the problem into a finite dimensional semidefinite programming problem. This framework does not require piecewise linear system matrices and funnel parameters, which is typically assumed in recent related work. We illustrate the proposed funnel synthesis method with a numerical example.

In this paper we consider finite-time stabilization and finite-time boundedness control problems for time-varying discrete-time systems. We give a set of sufficient conditions, in terms of differen...

In this paper, the finite-time stability analysis and stabilization for switched discrete linear system are investigated. A sufficient condition for finite-time stability of switched system is given by searching for a set of positive matrices which is less conservative than searching for a single positive matrix. Then the static-state feedback and dynamic output feedback finite-time stabilization are proposed. Several examples are given to illustrate the results within this paper.

Finite-time stability and stabilization of linear discrete time-varying stochastic systems

This study presents novel sufficient conditions for both finite-time and practical stability of the continuous linear control systems with latency in the state variables. The analyzed systems are mathematically represented using the state space differential equations with time delay. The new delay-independent finite time stability criteria were generated utilizing the Lyapunov-Krasovskii functional. This functional is not required to have non-negative definite properties on the entire state space. Furthermore, it is not required that the derivations of the functional are negative along the trajectories as it is the case for conventional stability conditions. Consequently, the presented conditions can be implemented in a practical calculation without difficulties.

In this paper, the problem of global asymptotic stability analysis for stochastic reaction-diffusion bidirectional associative memory neural networks (BAMNNs) with mixed delays and impulsive effects are investigated. The mixed delays consists of time delays in the leakage terms and continuously distributed delays. Based on the Lyapunov–Krasovskii functional (LKF), It's differential formula and linear matrix inequality (LMI) method, some sufficient conditions for global asymptotic stability in mean square of the equilibrium point of the systems are derived. The feasibility of the conditions are verified using the MATLAB LMI toolbox. Finally, two examples are provided to illustrate the effectiveness and validity of the derived main results.