Output feedback stabilization for a class of distributed parameter switched systems

Some sufficient conditions for exponential stability of linear neutral functional differential equations

The general model of distributed parameter switched systems (DPSS) was presented by means of operator semigroup theory. On condition that the infinitesimal generator operators of all subsystems satisfy multiplication commutative law, the sufficient conditions of exponential stability and switching laws were obtained for the DPSS consisting of subsystems with the same or various patterns. Meanwhile, the simulation experiment was conducted to test the models and theorem.

We study the problem of output feedback stabilization for stochastic nonlinear systems. We consider a class of stochastic nonlinear systems in observer canonical form with stable zero-dynamics. We introduce a sequence of state transformations that transform the system into a lower triangular structure that is amenable for integrator backstepping design. Then we design the output feedback controller and prove that the closed-loop system is bounded in probability. Under an infinite-horizon risk-neutral cost criterion, the controller designed can guarantee an arbitrarily small long term average cost. Furthermore, when the disturbance vector field vanishes at the origin, the closed-loop system is asymptotically stable in the large, and the risk-neutral cost is guaranteed to be zero. With special care, the controller preserves the equilibrium of the nonlinear system.

By using the stochastic optimization approach of Luus and Jaakola [1], a large class of stabilization problems can be readily solved. Application of the approach to the output feedback stabilization problem and the multivariable stability example of Anderson et al. [2] is discussed and illustrated.

This paper investigates the problem of output feedback stabilization for a class of stochastic feedforward nonlinear systems with time-varying input delay. The drift and diffusion terms satisfy the linear growth condition and are dependent on unmeasurable states and the delayed input. First, we use a change of coordinates to introduce a scaling gain into the system. Then, based on the high-gain observer technique, a delay-free output feedback controller with the scaling gain is developed. Based on the Lyapunov–Krasovskii method and the idea of feedback domination, it is shown that the closed-loop system can be rendered globally asymptotically stable in probability via appropriately choosing the scaling gain. Finally, two examples are presented to illustrate the effectiveness of the proposed scheme.

Uniform Parametric Convergence in the Adaptive Control of Mechanical Systems

Output feedback stabilization of nonlinear dual-rate sampled-data systems via an approximate discrete-time model

This study is concerned with the problem of exponential stability for a class of switched positive linear systems consisting of both stable and unstable subsystems. The sufficient conditions of exponential stability are established in continuous‐time and discrete‐time domains. Based on the average dwell‐time approach, new stability results for such kind of systems are first derived, which allows the ascent of the multiple linear copositive Lyapunov functions caused by unstable subsystems. Furthermore, when all subsystems are stable, the exponential stability condition for switched positive systems is presented. Finally, numerical examples are given to illustrate the effectiveness of the results.

In this paper, we deal with the problem of output feedback stabilization for a class of linear hybrid systems. This problem is addressed by characterizing the structural properties of such a class of systems. Namely, reachability, controllability, stabilizability, observability, constructibility, and detectability are framed in terms of algebraic and geometric conditions on the data of the system. Two canonical forms, recalling the classical Kalman decompositions with respect to reachability and observability, are given. By taking advantage of this characterization, duality between control and observation structural properties is established and necessary and sufficient conditions for the existence of a linear time-invariant output feedback compensator are stated. Compared with previous results, no assumption is needed on the plant about minimum phaseness, relative degree, or squareness.

This article considers the problem of output feedback stabilization for a class of stochastic high‐order nonlinear time‐delay systems with unknown output function. For stochastic high‐order nonlinear time‐delay systems, based on the Lyapunov stability theorem, by combining the addition of one power integrator and homogeneous domination method, the maximal open sector of output function is given. As long as output function belongs to any closed sector included in , an output feedback controller can be developed to guarantee the closed‐loop system globally asymptotically stable in probability.

Stability analysis of discrete-time switched linear systems with unstable subsystems

This correspondence paper addresses the problem of output feedback stabilization of control systems in networked environments with quality-of-service (QoS) constraints. The problem is investigated in discrete-time state space using Lyapunov's stability theory and the linear inequality matrix technique. A new discrete-time modeling approach is developed to describe a networked control system (NCS) with parameter uncertainties and nonideal network QoS. It integrates a network-induced delay, packet dropout, and other network behaviors into a unified framework. With this modeling, an improved stability condition, which is dependent on the lower and upper bounds of the equivalent network-induced delay, is established for the NCS with norm-bounded parameter uncertainties. It is further extended for the output feedback stabilization of the NCS with nonideal QoS. Numerical examples are given to demonstrate the main results of the theoretical development.

This paper investigates the problem of robust output feedback stabilization of uncertain Hamiltonian systems with saturating actuator and input delay. The uncertainties are assumed to be time invariant and belong to convex bounded polytopic domain. By employing Lyapunov-Krasovskii functional method and Wirtinger's inequality, some sufficient conditions are derived for stabilization of nonlinear Hamiltonian systems under consideration. A delay-independent condition in terms of linear matrix inequalities for control of the Hamiltonian systems is established first. And further, an output feedback controller synthesis scheme under the multiple Lyapunov functional framework is proposed which guarantees the robust stability of the closed-loop system when control saturation and delay effectively occur. Finally, numerical results are given to demonstrate the effectiveness of the proposed methodology.

In this paper, the problem of delay-dependent robust dynamic output feedback stabilization for a class of uncertain singular time-delay system is investigated. Based on the delay-dependent stability criterion for nominal singular time-delay systems and the concept of generalized quadratic stabilization, the sufficient conditions of the existence of the feedback controller are obtained, which ensure that the closed-loop systems are regular, impulse free and robustly asymptotically stable. Moreover, the expression for the desired robustly stabilizing controller is given by using the LMIs and the cone complementarity linearization iterative algorithm.

In this paper, the exponential stability analysis for ODE switched systems with time delay is extended to distributed parameter switched systems (DPSS) in Hilbert space. For a given family of exponential stable subsystems, this paper focuses on finding conditions to guarantee the overall DPSS’ exponential stability. Based on semigroup theory, by applying piecewise Lyapunov-Krasovskii functionals method incorporated average dwell time approach, sufficient conditions for exponential stability are derived. These conditions are given in the form of linear operator inequalities (LOIs) where the decision variables are operators in Hilbert space, and the stability properties depend on switching rule. Being applied to heat switched propagation equations, these LOIs are reduced to standard Linear Matrix Inequalities (LMIs). Finally, a numerical example is given to illustrate the effectiveness of the proposed result.