Andrew R. Teel

Small-gain theorem for ISS systems and applications

We introduce a concept of input-to-output practical stability (IOpS) which is a natural generalization of input-to-state stability proposed by Sontag. It allows us to establish two important results. The first one states that the general interconnection of two IOpS systems is again an IOpS system if an appropriate composition of the gain functions is smaller than the identity function. The second one shows an example of gain function assignment by feedback. As an illustration of the interest of these results, we address the problem of global asymptotic stabilization via partial-state feedback for linear systems with nonlinear, stable dynamic perturbations and for systems which have a particular disturbed recurrent structure.

A nonlinear small gain theorem for the analysis of control systems with saturation

A nonlinear small gain theorem is presented that provides a formalism for analyzing the behavior of certain control systems that contain or utilize saturation. The theorem is used to show that an iterative procedure can be derived for controlling systems in a general nonlinear, feedforward form. This result, in turn, is applied to the control of: 1) linear systems (stable and unstable) with inputs subject to magnitude and rate saturation and time delays; 2) the cascade of globally asymptotically stable nonlinear systems with certain linear systems (those that are stabilizable, right invertible, and such that all of their invariant zeros have nonpositive real part); 3) the inverted pendulum on a cart; and 4) the planar vertical takeoff and landing aircraft.

Control of linear systems with saturating actuators

This paper deals with the design of linear systems with saturating actuators where the actuator limitations have to be incorporated a priori into control design. The authors take a semiglobal approach to solve some of the central control problems for such systems. These problems include stabilization, input-additive disturbance rejection, and robust stabilization in the presence of matched nonlinear uncertainties. The authors develop further the semiglobal design technology which was initiated in their earlier work (Lin and Saberi, 1995) and utilize it to deal with these control problems.

Global stabilizability and observability imply semi-global stabilizability by output feedback

We show that smooth global (or even semi-global) stabilizability and complete uniform observability are sufficient properties to guarantee semi-global stabilizability by dynamic output feedback for continuous-time nonlinear systems.

Semi-global stabilizability of linear null controllable systems with input nonlinearities

An H/sub /spl infin//-based Lyapunov proof is provided for a result established by Lin and Saberi (1993): if a linear system is asymptotically null controllable with bounded controls then, when subject to input saturation, it is semi-globally stabilizable by linear state feedback. A new result is that if the system is also detectable then it is semi-global stabilizable by completely linear output feedback. Further, an extension which relaxes the requirements on the input characteristic is obtained. >

Singular perturbations and input-to-state stability

This paper establishes a type of total stability for the input-to-state stability property with respect to singular perturbations. In particular, if the boundary layer system is uniformly globally asymptotically stable and the reduced system is input-to-state stable with respect to disturbances, then these properties continue to hold, up to an arbitrarily small offset, for initial conditions, disturbances, and their derivatives in an arbitrarily large compact set as long as the singular perturbation parameter is sufficiently small.

Non-holonomic control systems: from steering to stabilization with sinusoids

We present a control law for globally asymptotically stabilizing a class of controllable nonlinear systems without drift. The control law converts into closed loop feedback earlier strategies for open loop steering of non-holonomic systems using sinusoids at integrally related frequencies. The global result is obtained by introducing saturation functions. Simulation results for stabilizing a simple kinematic model of an automobile are included.

Feedback Stabilization of Nonlinear Systems: Sufficient Conditions and Lyapunov and Input-output Techniques

This lecture is devoted to the survey of some recent results on feedback stabilization of nonlinear systems. This text can be seen as a prolongation of the overview written by E. Sontag in 1990 [83] in several directions where progress has been made. It consists of three parts: n n nThe first part is devoted to sufficient conditions on the stabilization problem by means of discontinuous or time-varying state or output feedback. n n nIn the second part, we present some techniques for explicitly designing these feedbacks by using Lyapunov’s method. This introduces us with the notion of assignable Lyapunov function and leads us to concentrate our attention on systems having some special recurrent structure. n n nThe third part presents some techniques for designing feedback based on L ∞ stability properties. This last section also addresses robustness through a small gain theorem.

The almost disturbance decoupling problem with internal stability for linear systems subject to input saturation—state feedback case

Abstract We consider the almost disturbance decoupling problem (ADDP) and/or almost D -bounded disturbance decoupling problem ((ADDP) D ) with internal stability for linear systems subject to input saturation and input-additive disturbance via linear static state feedback. We show that the almost D -bounded disturbance decoupling problem with local asymptotic stability ((ADDP/LAS) D ) is always solvable via linear static state feedback as long as the system in the absence of input saturation is stabilizable, no matter where the poles of the open-loop system are, and the locations of these poles play a role only in the solution of (ADDP/GAS) D , (ADDP/SGAS) D or ADDP/GAS where semi-global or global asymptotic stability is required.

Simultaneous L p -stabilization and internal stabilization of linear systems subject to input saturation—state feedback case

Abstract We consider the problem of simultaneous finite gain L p -stabilization and internal stabilization of linear systems subject to input saturation via linear static state feedback. We show that bounded input finite-gain L p -stabilization and local asymptotic stabilization can always be achieved simultaneously no matter where the poles of the open-loop system are, and the locations of these poles play a role only when bounded input finite gain L p -stabilization and global or semi-global stabilization are required simultaneously.