A nonlinear system possesses an invariancewith respect to a set of transformations if its output dynamics remain invariant when transforming the input, and adjusting the initial condition accordingly. Most research has focused on invariances with respect to time-independent pointwise transformations like translational-invariance (u(t) → u(t) + p, p ∈ R) or scale-invariance (u(t) → pu(t), p ∈ ...

This paper considers the robust stability of a discrete-time Lurye system consisting feedback interconnection between linear and bounded monotone nonlinearity. It has been conjectured that existence suitable time-invariant (LTI) O’Shea–Zames–Falb multiplier is not only sufficient but also necessary. Roughly speaking, successful proof conjecture would require: (a) conic parameterisation set mult...

In this paper, new Lyapunov-based reset rules are constructed to improve L2 gain performance of linear-time-invariant (LTI) systems. By using the hybrid system framework, sufficient conditions for exponential and finite gain L2 stability are presented. It is shown that the L2 gain of the closed loop system with resets can be improved compared with the base system. Numerical example supports our...

We propose an Approximate Implicit Subspace Iteration with Alternating Directions (AISIAD) framework for Linear Time Invariant (LTI) system model reduction. Within this framework, dominant eigensubspaces of the product of the system Gramians are approximated directly. This has advantage over approaches that consider the system Gramians separately. We construct two methods within the framework, ...

A general multirate lter-bank system with multiple channels and nonuniform bands is studied with the reconstruction performance measured by the worst-case energy gain (H 1 norm) of the error system between the multirate system and a pure time-delay system. Using blocking and polyphase decomposition, we associate with the multirate system an equivalent linear time-invariant (LTI) system whose tr...

Methods for index reduction of general nonlinear differential-algebraic equations are generally difficult to implement due to the recurring use of functions defined only via the implicit function theorem. By adding structure to the equations, these implicit funcitons may become possible to implement. In particular, this is so for the quasilinear and linear time-invariant (LTI) structures, and i...

The problem of remotely controlling an unstable noiseless linear time invariant system over noisy half-duplex relay channels with average power constraints is considered. For information transmission, we propose a coding scheme based on the Schalkwijk-Kailath scheme. Therefore, we derive conditions on rate which are sufficient for mean square stability of the linearly controlled LTI system over...

This paper deals with structurally constrained periodic control design for interconnected systems. It is assumed that the system is linear time-invariant (LTI), observable and controllable, and that its modes are distinct and nonzero. It is shown that the notions of quotient fixed mode (QFM) and structured decentralized fixed mode (SDFM) are equivalent for this class of systems. Then, it is pro...

In this paper, we analyze stability and L2 gain properties for discrete-time linear time-invariant (LTI) systems controlled by a pre-designed dynamical output feedback controller which fails from time to time due to physical or purposeful reason. Our aim is to find conditions concerning controller failure time, under which the system’s stability and L2 gain properties are preserved to a desired...

In this paper, we focus our attention on linear time invariant continuous time linear systems with one input and one output (SISO LTI systems). We consider the problem of constructing a reduced order system via truncation of the original system. Given a SISO strictly proper transfer function T (s) of McMillan degree N and a strictly proper SISO transfer function T̂ (s) of McMillan degree n < N ,...