Stability Of Nonlinear Control Systems Research Articles

Homogeneous Lyapunov functions and necessary conditions for stabilization

We provide necessary conditions for the stabilization of nonlinear control systems with the additional requirement that a time-invarianthomogeneous Lyapunov function exists for the closed-loop system.

Application of a two-step compensating scheme to a class of nonlinear control systems

The stabilization problem of a class of nonlinear control systems via dynamic output feedback is investigated in this paper. The paper contains some original results for the stabilization of nonlinear control systems, established by applying the factorization theory for linear systems and quasi-stability results of Persidskii.

Feedback stabilization of nonlinear systems by locally bounded controls

In this paper results are presented on output regulation and stabilization of nonlinear control systems using Lyapunov-based methods. Sufficient conditions for global output regulation and stabilization using locally bounded state feedback are obtained. The approach used here is motivated by the work of Artstein (1983), Sontag (1989) and Tsinias (1989) on the relationship between control Lyapunov functions and feedback stabilization.

Symbolic computation approach for absolute stability

A criterion for absolute stability of nonlinear control systems, which is equivalent to Popov's criterion, is given. The condition for absolute stability can be tested without graphics. Symbolic computation is employed for the test. A Maple program and some examples are given.

050 Practical stabilization of nonlinear control systems

050 Practical stabilization of nonlinear control systems

Practical Stabilization of Nonlinear Control Systems

In this paper, a nonlinear control system is said to be practically stabilizable if for an arbitrary small region V around the equilibrium point, there exists an analytic feedback control which confines the closed loop trajectory starting from a initial point x o in some bounded region Ω. And a nonlinear system is said to be weakly practically stabilizable if the closed loop trajectory is confined in some region ∪ ⊂ Ω. Some sufficient conditions for the practical stabilizability have been derived by applying the system decomposition called the virtual decomposition.

Comments on: 'Stability of nonlinear control systems: the "impulse momentum" method'

Comments on: 'Stability of nonlinear control systems: the "impulse momentum" method'

On robust stabilization of nonlinear control systems

A robust stabilization problem for general MIMO nonlinear systems is formulated in a Banach space setting in the time domain. Existence and uniqueness theorems are established, a general procedure for solving the problem is illustrated, and a simple example is included to show how the results can be applied.

Stabilization of non-linear control systems: the role of Newton diagrams

Abstract The stabilization of two-dimensional non-linear control systems is treated, although the main technique is applicable to more general systems. It combines the theory of centre manifolds and singularities of algebraic functions to design continuous, but not necessarily Lipschitz, stabilizing feedback control laws. In particular, the devices known as the Newton diagram and the Newton or Puiseux polygon are employed to construct uniformizing transformations. Finally, remarks are made about systems for which no continuous stabilizing feedback control law exists.

Stabilization of non-linear control systems: the role of Newton diagrams

Stabilization of non-linear control systems: the role of Newton diagrams

Stabilization of nonlinear systems with uncontrollable linearization

The problem of local stabilization of nonlinear control systems with linearizations that contain uncontrollable modes on the imaginary axis is considered. A methodology of designing a stabilizing control is investigated. It involves the following steps: (1) reduction of the stability problem to the stability of the center manifold system, (2) simplification of the vector field on the center manifold using the theory of normal forms, and (3) finding conditions under which the simplified vector field is asymptotically stable. Three cases of degeneracies in the linearized system are treated, and sufficient conditions for the existence of stabilizing controls are given in each case. A theorem is presented regarding the robustness of the above control strategies. >

Stabilization of non-linear control systems to subspaces

Abstract The property is studied of stabilizing a polynomial control system to a subspace of its state space using a continuous feedback law. A sufficient condition for the output stabilizability problem is also included.

Method of power transformations for analysis of stability of nonlinear control systems

New frequency-domain criteria for absolute stability are obtained. These criteria essentially improve the estimates of stability regions in the parameter space compared with well-known results of V.M. Popov (1961,1973) and the circle criterion of J.J. Bongiorno (1964).

Stability Bounds for Nonlinear Systems Designed Via Frequency Domain Stability Criteria

Compensator design results are compared for the circle and Popov criteria, both of which are sufficiency conditions for absolute stability of nonlinear control systems. Analog simulation studies yielded higher compensator gains than either of the two criteria. Nevertheless, the analog results showed the same general trend as the circle and the Popov criteria results. The circle criterion was found to be more conservative than the Popov criterion in the numerical examples presented here.

On cross coupling and stability in nonlinear control systems

A stability criterion for cross-coupled symmetrical two-dimensional nonlinear systems is presented. The effect of cross coupling on the stability of the system is discussed.

A New Circle Criterion for the Stability of Nonlinear Control System

A New Circle Criterion for the Stability of Nonlinear Control System

Stochastic stability in nonlinear control systems

The stability of nonlinear control systems with stochastic coefficients is studied by applying the Lyapunov theory. A Lyapunov function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V(x)</tex> is first assumed, similar to the deterministic case. Consider next the natural stochastic analog of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\dot{V}(x)</tex> as à <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V(x)</tex> , where à is equal to the differential generator. The procedure of establishing stability conditions is illustrated by two second-order examples and four third-order examples.

Absolute stability of nonlinear control systems with time lag

A nonlinear control system with time lag is transformed into a nonlinear control system with no time lag by means of certain types of transformations. If absolute stability for this transformed nonlinear control system is obtained by Popov's method, absolute stability in the nonlinear control system with time lag is realized.

Book Review: Stability of Non-linear Control Systems

Book Review: Stability of Non-linear Control Systems

Stability of Nonlinear Control Systems

Stability of Nonlinear Control Systems