On the Stability and Estimation of Ultimate Boundedness of Nonlinear/Uncertain Dynamic Systems with Bounded Controllers

1990 ◽  
Author(s):  
Mehrez Hached ◽  
S. Mehdi Madani-Esfahani ◽  
Stanislaw H. Zak
Keyword(s):  
Dynamic Systems ◽  
Ultimate Boundedness ◽  
Uncertain Dynamic Systems ◽  
The Stability

Structural Decomposition Approach for the Stability of Uncertain Dynamic Systems

1988 ◽  
Vol 55 (4) ◽  
pp. 992-994 ◽  
Author(s):  
Y. H. Chen ◽  
Chieh Hsu
Keyword(s):  
Dynamic Systems ◽  
A Priori ◽  
Parameter Variation ◽  
Stability Study ◽  
Fast Time ◽  
Time Varying ◽  
Decomposition Approach ◽  
New Approach ◽  
Uncertain Dynamic Systems ◽  
The Stability

The stability property for a class of dynamic systems with uncertain parameter variation is studied. The uncertainty can be fast time-varying and unpredictable. A new approach for stability study is proposed. The only required information on the uncertain variation is its possible bound as well as structure. That is, no a priori knowledge on the realization of the variation is needed.

scholarly journals Stability of conditionally invariant sets and controlled uncertain dynamic systems on time scales

1995 ◽  
Vol 1 (1) ◽  
pp. 1-10 ◽  
Author(s):  
V. Lakshmikantham ◽  
Z. Drici
Keyword(s):  
Time Scales ◽  
Dynamic Systems ◽  
Invariant Sets ◽  
Continuous Systems ◽  
Stability Properties ◽  
Closed Sets ◽  
Controlled Systems ◽  
Uncertain Dynamic Systems ◽  
Imperfect Knowledge ◽  
The Stability

A basic feedback control problem is that of obtaining some desired stability property from a system which contains uncertainties due to unknown inputs into the system. Despite such imperfect knowledge in the selected mathematical model, we often seek to devise controllers that will steer the system in a certain required fashion. Various classes of controllers whose design is based on the method of Lyapunov are known for both discrete [4], [10], [15], and continuous [3–9], [11] models described by difference and differential equations, respectively. Recently, a theory for what is known as dynamic systems on time scales has been built which incorporates both continuous and discrete times, namely, time as an arbitrary closed sets of reals, and allows us to handle both systems simultaneously [1], [2], [12], [13]. This theory permits one to get some insight into and better understanding of the subtle differences between discrete and continuous systems. We shall, in this paper, utilize the framework of the theory of dynamic systems on time scales to investigate the stability properties of conditionally invariant sets which are then applied to discuss controlled systems with uncertain elements. For the notion of conditionally invariant set and its stability properties, see [14]. Our results offer a new approach to the problem in question.

Robust Control of Generalized Dynamic Systems Without the Matching Conditions

1991 ◽  
Vol 113 (4) ◽  
pp. 582-589 ◽  
Author(s):  
Zhihua Qu ◽  
John Dorsey
Keyword(s):  
Robust Control ◽  
Dynamic Systems ◽  
Control Law ◽  
General Control ◽  
Matching Conditions ◽  
Uncertain Dynamic Systems ◽  
Special Cases ◽  
The Stability ◽  
Bounded Uncertainties

A general control law and a set of conditions are proposed to guarantee the stability of dynamic systems with bounded uncertainties. The results do not require the matching conditions on the uncertainties and subsume several existing results as special cases. Moreover, it is shown that there is at least one class of uncertain dynamic systems which can always be stabilized under the proposed control law no matter what the size and the structure of the input-unrelated uncertainties.

Convergence Rates of a Class of Uncertain Dynamic Systems

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Juan Ignacio Mulero-Martínez
Keyword(s):  
Dynamic Systems ◽  
Uncertain Systems ◽  
Convergence Rates ◽  
Initial Conditions ◽  
Compact Set ◽  
Robust Nonlinear Control ◽  
Riccati Differential Equation ◽  
Uncertain Dynamic Systems ◽  
Complete Treatment ◽  
The Stability

The problem of stabilization of uncertain systems plays a broad and fundamental role in robust control theory. The paper examines a boundedness theorem for a class of uncertain systems characterized as having a decreasing Lyapunov function in a ringlike region. It is a systematic study on stability that embraces both the transient and steady analysis, covering such aspects as the maximum overshoot of the system state, the stability region and the exponential convergence rate. The emphasis throughout is on deriving dominant time constants and explicit time expressions for a state to reach an invariant set. The central theorem provides a complete treatment of the time evolution of trajectories depending on the specific compact set of initial conditions. Toward this end, the comparison lemma along with a particular Riccati differential equation are essential and conclusive. The scope of questions addressed in the paper, the uniformity of their treatment, the novelty of the proposed theorem, and the obtained results make it very useful with respect to other works on the problem of robust nonlinear control.

Sign in / Sign up

Export Citation Format

Share Document